Instead, those teams are reportedly discussing Francisco Rodriguez, a man who once assaulted his father-in-law at Citi Field and did not sign a major-league deal this season until April 17. The Phillies are insistent on retaining Papelbon, even as they straddle contention.
And, even if the Phillies were willing to assume some of the many dollars to be paid on Papelbon's four-year, $50 million contract, the interest might be lackluster. That is a grim harbinger for a contract not even halfway completed.
The signs of decline for the 32-year-old righthander are everywhere but in the traditional numbers. Scouts have whispered about their concerns. Papelbon's fastball velocity averaged 95 m.p.h. in 2011. It was 93.8 m.p.h. in 2012 and has dipped to 92.4 m.p.h. in 2013. He is striking out 7.91 batters per nine innings, a career-low rate. He averaged 10.8 strikeouts per nine innings before 2013.
The fewer strikeouts Papelbon records, the more balls that are put in play. That makes luck a higher variable in the equation. He has enjoyed good fortune in 2013; opponents are batting .238 on balls in play. (The league average is typically around .300. Papelbon's average is .282.)
The larger concern is what Papelbon represents, the overvaluing of closers in modern baseball. Consider this: The Phillies have converted 64 of 94 (68.1 percent) save opportunities since Papelbon signed. The major-league average in that same span is 69.5 percent. In 2009, when Brad Lidge stumbled to a 7.51 ERA as a closer, the Phillies converted 66.7 percent of save opportunities. They were at 83.9 percent in 2011 when Lidge and Jose Contreras were both anointed closer and suffered injuries.
Papelbon is not responsible for all of the blown saves in the last two seasons. But that is what happens when $50 million is devoted to one relief pitcher who throws an average of 66 innings per season. The rest of the bullpen is patchwork. One failed signing, like Mike Adams, and chaos consumes the unit.
A long-term contract for a closer is not prudent. Research by ESPN.com showed that three teams employ the same closer in 2013 as they did in 2011. They were the Yankees (Mariano Rivera), the Indians (Chris Perez) and the Braves (Craig Kimbrel). The staying power of a closer is remarkably fickle.
Papelbon has complained of hip soreness and general fatigue this season. Manager Charlie Manuel said overuse is a concern.
"I don't like to pitch him for four or five outs," Manuel said. "That really can burn him out. It used to burn Billy Wagner out. It burned out quite a few pitchers I had. That way, you can have him for three or four days in a row.
"We have to have our pitchers for three days in a row, at least. Any one-inning guy in your bullpen, you need them to be able to pitch three days in a row. We haven't been getting that out of ours."
Had the Phillies invested the money earmarked for Papelbon in four one-inning relievers over two winters, Manuel could oversee a more efficient bullpen. The hot hand could be his closer. If there are injuries, like in 2011, trusted arms instead of inexperienced ones serve as replacements.
That was but a mere fantasy on a sweltering day as J.C. Ramirez and Jake Diekman surrendered a crucial seventh-inning run. The bullpen door opened at 4:46 p.m., and Papelbon emerged unused as the Mets celebrated victory.
Contact Matt Gelb at email@example.com. Follow on Twitter @magelb.