Not only did the Angels deal for Vernon Wells and the $86 million left on his contract, but they also gave away Mike Napoli and Juan Rivera. All right, so that's the best possible hope for a trade involving Markakis: getting another team to take his contract AND getting a couple of players in return. But Markakis also has much less money remaining on his deal ($44 million, including a $2 million buyout on his $17.5 million 2015 club option), is five years younger, and is probably better than Wells.
Like I said before, it won't be easy, but there's a chance. Maybe the Angels are interested.
Salary information, as always, via Cot's Baseball Contracts.