AJ Burnett is likely to be a pretty sought after free agent. Lets look at some teams that could be interested.
Yankees (frontrunner) The Yankees will go extremly hard after Burnett if they haven’t already signed CC Sabathia or Ben Sheets. They will probably sign one of those two, though, making Burnett unlikely.
Mets (frontrunner) The Mets need starting pitching, it is their offseason priority. If they miss out on other options, Burnett could be their man. The Mets are probably going to be in on every starter on the market as they try to fill the hole left by Oliver Perez. Burnett makes a lot of sense here.
Red Sox (frontrunner) The Red Sox don’t need starting pitching, but they can seperate themselves from other teams with this signing, or if they get a better one like CC or Sheets. If those two sign elsewhere, then Burnett makes a lot of sense.
Cardinals (possible) They have a need at starting pitcher, and almost signed him last time he was in free agency. They could go after him again. However, the last thing they need is another injury prone starter. And they usually don’t spend a lot of money on free agents.
Phillies (possible) They had interest in him at the trade deadline and could go after him again in the offseason. Burnett still makes a lot of sense for this team if they can afford him.
Blue Jays (possible) It is possible that Burnett exersises his 24 million player options. It has been said that the Jays could pay Burnett an extra 4 to 6 million to entice him to not opt out. So, essentially offer him 2 years, 30 million. I don’t think Burnett would take this, anyway.
Nationals (slim chance) Burnett could chose to sign close to his home if he hooks on with the Nats. But, they might not offer enough money, and probably wouldn’t want to make a big free agent signing, rather save up for Stephen Strasburg.
Oriols (dark horse) The Oriols are the dark horse because they could end up signing him. If they want to accelerate the rebuilding by signing a free agent, they could look into Burnett. Burnett lives in Baltimore and could take a small discount to sign there.