One closer the Mets could look to bring in is Joel Hanrahan.
After two dominant seasons as the Pirates' closer in 2011 and 2012, the Pirates traded Hanrahan to the Red Sox last offseason. Unfortunately, 2013 was a lost year for Hanrahan, who struggled in April and had a 9.82 ERA in nine appearances before having to undergo season-ending surgery on his forearm.
The eventual world champion Red Sox later found Koji Uehara to be their new closer for the rest of the season, while Hanrahan was unable to pitch and did not end up being too relevant in the Red Sox's championship run.
Hanrahan is now a free agent, and it's very unlikely that a return to the Red Sox will be happening. A team like the Mets, however, should look into signing him in order to strengthen their bullpen. A late-inning duo of Hanrahan and current closer Bobby Parnell could be very effective for the Mets if it were to happen.
Furthermore, Parnell himself had surgery on his neck in September. Parnell should be healthy by spring training, but in case he isn't, it would be good for the Mets to have another reliever with legitimate closing experience. A healthy Hanrahan could fit the bill there for sure.