It's been a rough season-and-a-half for Lucas Duda. When he belted 21 homers in 301 ABs in 2011, the Mets thought they had the makings of slugger. Then Duda struggled to start 2012 and spent a good portion of his summer in Buffalo. So far 2013 has been an up and down season for him; he's hit a respectable 11 longballs and shown a decent amount of plate discipline, but his offensive prowess has been maddeningly inconsistent. He's also proven himself a potential menace in the field, no matter which position he's forced into. Duda has been on the DL since June 22 with an intercostal strain, and as of last Friday he had yet to resume baseball activities. Contract-wise, Duda remains a pre-arbitration player through next season, with arbitration years 1, 2, and 3 to follow in 2015–2017.
Last off season, the Mets said Duda was part of their long-term plans, but considering his struggles and how much rebuilding the team has yet to do, he would have to be expendable if the right deal came along. The biggest wrinkle is that Duda is currently on the DL and intercostal strains are notoriously slow healing. Add to this the return of Ike Davis and a crowded outfield and it's anybody's guess how much playing time Duda will get before the trade deadline to prove he can be useful for another team, or if he returns before July 31 at all.
Considering Duda's glove skills (or lack thereof), he would be most attractive for an AL team with injury issues looking for short-term stretch-drive help at DH/1B. Boston could use him to give more rest to David Ortiz, who's dealing with heel problems, or the Yankees could use him to deal with Everyone Else Is Hurt Problems. Texas might need some bench assistance now that Lance Berkman has hit the DL. On the NL side, Duda might be tempting for Colorado if Carlos Gonzalez has to miss any appreciable amount of time. If the Reds were reportedly considering a deal with the recently DFA-ed Jeff Francoeur, Duda would have be an upgrade to that scenario for Cincinnati.
On the one hand, Duda will be cheap and under control for the next four seasons. On the other hand, he's Lucas Duda. Complicating matters is the fact that that all of the teams named above will have much larger priorities at the deadline than the hole(s) Duda can fill. So you'd have to think Duda could only be exchanged for a player of a similar profile: not a prospect, but someone who's either (1) without a real position; (2) roadblocked by more established players; or (3) struggled to make the transition to the bigs. Barring that, a mid-level farmhand or two.
Of all potential trade partners, Boston has the most robust farm system and can probably most afford to "overpay" for a potential quick fix. Alex Hassan, an OF/1B, is the kind of player you'd expect in exchange for Duda—a player with good plate discipline but some injury issues who's boxed out of the team's plans at the moment by better prospects. However, the Sox seem to be concentrating on pitching as July 31 approaches and will most likely use their bonanza of minor league talent for that end. They were even said to be willing to take on Ryan Howard's contract in a deal for Cliff Lee (before Howard went on the DL for meniscus surgery), which indicates the Sox would like to make a bigger splash at the deadline than acquiring Lucas Duda.
The Mets and Yankees are usually loath to help one another out, and the Yanks have virtually no one of value to trade who's not on the DL, so a deal between the two seems unlikely. Like the Sox, the Rangers have bigger fish to fry and are reportedly looking at Matt Garza and Giancarlo Stanton. Their weak division notwithstanding, the Rockies have gone through a dreadful stretch lately that may have removed them from the ranks of buyers. As for the Reds, they are reportedly interested in acquiring Michael Morse from the Mariners for outfielders Chris Heisey and Miguel Robinson, plus a prospect. The Mets would probably gladly take that for Duda, but the Reds would, in all likelihood, rather have Morse.
My best guess is Duda's injury plus the small-ish haul he'd bring back add up to him being a Met for the foreseeable future.