The 28-year-old has been with the Rays since being promoted for the club's World Series run in 2008. Over the next five seasons, he's gone 71-39 with a 3.21 ERA in 959 innings for the club, and won the AL Cy Young award in 2012.
He's eligible for arbitration next season as well, and is almost certain to get another substantial raise. At $14 million, Price would represent about twenty percent of the team's payroll. If they decide not to trade him, their payroll could end up somewhere around $70 million for the 2014.
Price has consistently appeared in trade rumors due to the unlikelihood that the small-market Rays will be able to extend him beyond 2015. The team could decide to keep Price this season since they are in a position to remain competitive in the AL East, but their ace's trade value is likely to diminish as he approaches the open market.
This offseason, the Dodgers have been linked to Price, but they appear to be more focused on the bidding for Masahiro Tanaka at the moment. If they are unable to land Tanaka, Los Angeles could have a renewed interest in trade talks with Tampa Bay. The Mariners and Cubs have also appeared in speculation on a possible move. However, teams have told the Rays they would require a contract extension with Price if they were to acquire him, an idea Price has shot down in the past.
At this point in the offseason, Rays general manager Andrew Friedman has said he's only "tinkering" with the team's roster for the 2014 season, but that could change if he gets the right offer on the trade market.