Wright is expected to be paid $16 million in 2013 after a season in which he hit .306 with 21 home runs and 93 runs batted in.
Dickey, set to collect $5 million next season, posted a 20-6 record with a 2.73 earned run average and 230 strikeouts. He is considered one of the frontrunners for the NL Cy Young Award. Dickey had surgery Oct. 18 to repair a torn abdominal muscle.
Mets General Manager Sandy Alderson has said a team priority is to work out new long-term contracts with both players.