The Wild could be well-served by adding a defenseman with experience. Ger has already looked at some available UFA Defensemen, and Tony has looked at a good internal option to fill the void. I'm going to look at the other way the Wild could go about acquiring a defenseman: trade.
The Wild have the benefit of not needing to add a top-pairing defenseman (not that they would turn down Duncan Keith if he rolled into the X and said "gimme a contract"). None of the young players are proven in the NHL, however, and that could leave their bottom pairing exposed if none of them are ready for the Big Show.
There are 3 teams who are above the salary cap, all of whom could be looking to move some salary. Let's take a look at those three: the Philadelphia Flyers, the Chicago Blackhawks, and the Tampa Bay Lightning.
The Flyers have a number of defenseman without No-Trade Clauses: Mark Streit, Andrew MacDonald, Kimmo Timonen, and Nick Schultz.
Looking at that list, we can safely cross off Andrew MacDonald; he's a not exactly a brilliant #FancyStat player, and is only 23; the Wild aren't interested in him realistically. Erik Gustafsson is an RFA at the end of next season, and he isn't the large, physical-type that the Wild are supposedly looking for.
Mark Streit: He's 39 and highly-paid, with 3 years left on his contract. This puts him at 42 at the end of his contract, which is worth 5.25M per year. It's hard to see the Flyers trading Streit. He's a fantastic player, and has been brilliant from a Corsi perspective. The only reason I could see the Flyers moving Streit is to dump his salary, and if they did, the price would be more than the Wild are likely willing to give up.
Kimmo Timonen: He's also 39, though is less expensive with only 2M on his contract. He also only has 1 year left on his contract. A trade here is more possible; at Kimmo's age, it's possible he will start to decline. However, that decline hasn't happened yet. Unfortunately, the Flyers are just over $3 Million over the cap, and this doesn't quite get them out of trouble; it helps, but it isn't a full solution.
Nick Schultz: Wild fans are likely familiar with Mr. Schultz. He has 1 year left on his contract at 1.25M. Schultz has been less than stellar from a Corsi point of view, and a return to the Wild, while possible, is unlikely. At 6'2'' and 200 pounds, Schultz is not small, but not huge. What's more, this trade won't cost as much as some other defensemen might cost, simply because of his less-than-stellar status.
Of these three options, the one that is most intriguing to me is Timonen. He is an older player who the Wild could trade for, and his contract means he would only be around for a year with a modest cap hit. 2 Million is a bit much for a 3rd-liner, but the benefit/cost ratio to bridge to some of the Wild's younger players is there.
What's more, the Flyers are looking to sell; they are moderately deep at the blue line, with lots of young players who are going to be looking for NHL time. Even better, the Flyers don't want to add more of a cap hit than they need to to replace whoever they move. My guess would be that a combo of young players and picks, with some cash, would be enough.
The Blackhawks are far less deep at D-men than the Flyers (in terms of sheer numbers). Yes, they have stars like Brent Seabrook, Duncan Keith, Niklas Hjalmarsson, and Johnny Oduya, but all of those (and Michal Rozsival) have an NTC or NMC in their contract. In fact, the only two defensemen currently under contract without an NTC are #WildKiller Nick Leddy and David Rundblad (Sheldon Brookbank is a UFA currently).
The Blackhawks also, however, have a sizable group of youngsters who are moving towards NHL readiness- namely, James Van Riemsdyk's younger brother Trevor.
Nick Leddy: Mr. Leddy is very familiar for most Wild fans. The 5'11'' 180-pound Eden Prairie man was drafted in the first round by the Wild in 2009, but was traded to Chicago for Cam Barker. Leddy has been a positive Corsi player every season and postseason since 2010-11, and has been a positive CF%Rel player each season and postseason except one. Unfortunately, Leddy is only 23, and the Blackhawks likely aren't interested in trading such a young player who shows such promise.
David Rundblad: Rundblad was also drafted in 2009 (by the Blues). He carries a cap hit of $785,000, is 6'2'' and 195 pounds. Similar to Leddy, it is doubtful that the Hawks are looking to move Rundblad, and doing so wouldn't benefit their cap situation much if they did.
The Blackhawks, most likely, are looking to move a forward. If the Wild look to Chicago for a defenseman, they have to hope either the Hawks are willing to part with Leddy, or one of their other blue liners is willing to waive their NTC. In short: likely, there are no trades to be had here, as Leddy would probably be more expensive than the Wild are willing to pay.
The Lightning are quickly becoming one of the scarier teams in the league. They have a number of Defensemen with NTC's, including Anton Stralman, Jason Garrison, Matt Carle. They do have a number without NTC's, however.
The Lightning's D-men without clauses are: Victor Hedman, Radko Gudas, Mark Barberio, and Andrej Sustr.
Victor Hedman: Hedman is 23, carries a hit of 4 Million, but is a very capable player. It's unlikely the Lightning are willing to move him. Even if they were willing, Hedman is a bit overkill for the hole the Wild are looking to fill.
Radko Gudas: Radko (who has maybe the coolest name of all time), is a 24-year old, 6'1'', 200-pounder. He is exactly the kind of player the Wild are looking for in terms of build (big and physical), and his low cap hit (under 1 Million) is appealing. The question comes in whether Gudas is a decent player or not. He has one great season and one mediocre-at-best season. My guess is the Wild aren't interested in Gudas simply because they are already log jammed with young defenseman.
Mark Barberio and Andrej Sustr: Neither of these options are appealing to the Wild: Barberio is a great young player who the Lightning like, and he would cost more than the Wild want to give up. Sustr is very similar to Gudas; young and inconsistent.
The Lightning don't have much to offer the Wild on the blue line. This is because the Wild already have young, promising defensemen, and because the Lightning don't have players that fit the role the Wild need filled.
The Wild are in a very unique situation. They don't want to pay as much as a top-pairing defenseman would cost, nor do they necessarily need to add a top-pairing player. They are simply looking for someone to play bottom-pairing minutes while the youngsters finalize their preparations. Assuming the Wild's front office thinks this way as well, the only player I could see them making a play for would be the Flyer's Timonen. It's possible Chuck Fletcher brings Nick Schultz back to Minnesota, but he is very similar to players that are available in free-agency, and there's no reason to give up pieces to acquire a middling player.
Ultimately, I doubt the Wild are going to make a move regarding the blue line in the offseason, unless it's an offer they can't refuse. I would bet some money (not a lot, but some) that the Wild start the season with the roster they have on the blue line, and if none of the youngsters can handle 3rd-pairing minutes, then they might make a move to bring in some experience.
If you haven't read Tony's article about Dumba yet, go do it, it's wonderful.
Edit: re-worded section around Andy Macdonald. Sarcasm doesn't work sometimes.