Pestano, 27, went 3-3 with a 2.57 ERA in 70 relief appearances for Cleveland in 2012, allowing only seven home runs and 24 walks in 70 innings. He isn't eligible for arbitration until next winter.
Rubin says the Mets were interested in Joel Peralta before he re-signed with Tampa Bay, and are attempting to engage the Royals in talks for bullpen help as well.
Pestano is a sinkerballer who does an outstanding job keeping the ball in the park. He throws his fastball in the low 90s but also throws a heavy curveball to complement his two other main pitches. He is cheap and under control for a while - he isn't eligible for free agency until after the 2016 season. If the price is right in trade, Pestano could be a low-risk upgrade to a bullpen lacking experience.