Popular with Mets fans, Dickey perturbed team management when he spoke about his contract situation last week during a club event at Citi Field for children displaced from their schools by Superstorm Sandy.
Dickey said he enjoyed playing for the Mets and added it would be "disappointing" if he went through his option year without a new deal and became a free agent.
"If that's the decision that they make, I feel like it would be unfortunate because it probably is going to mean that I'm not going to be back," Dickey said then. "And that would be sad."
Buck was an All-Star with Toronto in 2010. The 32-year-old hit .192 with 12 home runs and 41 RBIs for Miami last season, then was part of the big trade between Marlins and Blue Jays.
The 20-year-old Syndergaard went 8-5 with a 2.60 ERA for Class A Lansing. The 18-year-old Becerra hit .250 with four RBIs in 11 games in the rookie Gulf Coast League.
Thole hit .234 with one homer and 21 RBIs in 104 games last season. The 26-year-old played four seasons with the Mets.
Nickeas split last season with the Mets and Triple-A Buffalo. The 29-year-old hit .174 with one homer and 13 RBIs for New York.