Besides just the closer role, the Mets' bullpen altogether needs a makeover once again. This will continue the recent annual trend of completely remaking the Mets' bullpen each offseason.
The Mets' bullpen was not particularly good in the 2012 season and thankfully a few of its members, such as Ramon Ramirez and Jon Rauch, will not be returning in 2013. The Mets' bullpen was second to last in all of baseball last season with a 4.65 ERA. Only the Brewers had a worse bullpen and not by much with a 4.66 ERA. The Mets' bullpen's 19 blown saves was also not good as well.
As of right now, likely candidates for the Mets' 2013 Opening Day bullpen include Frank Francisco, Bobby Parnell, Josh Edgin and Robert Carson. Jeremy Hefner could once again be the Mets' long reliever and make occasional spot starts like he did this past season. If Hefner is included, that would be five spots in the Mets' bullpen, which could leave two spots up for grabs.
One of those spots could be filled by either Jeurys Familia or Jenrry Mejia. Both have had more experience as starting pitchers, but due to the Mets' depth in starting pitching, plus the fact that both of these pitchers are best known for their fastballs, both are more likely to become relievers in the long run.
Familia and Mejia are rather similar as pitchers, so it would be reasonable to expect one to be in the Mets' bullpen and the other to possibly get traded. Mejia though would be the better trade option between the two because he would likely get the Mets a better deal in return, due to the fact that he pitched in the Mets' bullpen for much of 2010 and also has more minor league experience as a starter. Nonetheless, both hurlers could end up becoming future closers down the road, whether it be with the Mets or for another team.
Assuming one of Familia or Mejia is in the Mets' bullpen to start the season, the Mets would then have a long reliever (Hefner) a right-handed short reliever (Familia or Mejia), a left-handed short reliever (Carson), a right-handed set-up man (Parnell), a left-handed set-up man (Edgin) and a closer (Francisco). The final spot is one that will likely be given to someone on the open market that the Mets will try to sign to a relatively cheap one- or two-year contract.
It's definitely possible that the Mets will sign a new reliever during the winter meetings. It may not be a new closer, but hopefully it will be someone that can help the Mets' bullpen improve.