The second is that Boston's bullpen has struggled in recent weeks and is missing a key reliever in Koji Uehara, who is out indefinitely with a strained pectoral muscle.
Red Sox manager John Farrell served as Papelbon's pitching coach from 2007-10, and the two enjoyed a strong working relationship.
From 2006-11, Papelbon racked up 219 saves with Boston, placing him well ahead of Bob Stanley (132) for the team lead.
Of course, Papelbon isn't pitching close to that level these days, which is why the Nationals released him.
As of July 23, Papelbon had a 2.56 ERA, but things spiraled downhill for him quickly after that. In his final five outings for the Nationals, he gave up nine hits and nine runs (eight earned) over 3 1/3 innings while walking five and striking out two, showing diminished velocity.
His ineffectiveness led to the Nats trading for Mark Melancon prior to the Aug. 1 non-waiver Trade Deadline.
Given that the Red Sox could sign Papelbon for the pro-rated minimum, there would be little risk in attempting a reunion if there was a roster spot available.
"We haven't had any discussions on Jonathan Papelbon," Farrell said. "I appreciate where you're going with that. We know he's a free agent, we know he's out there. Like I said, with any person or any player that's available, we'll certainly talk about it. That's yet to be had."
If the Red Sox decided to re-sign Papelbon, it would be as a setup man for Craig Kimbrel.
Brad Ziegler, Matt Barnes, Junichi Tazawa and Robbie Ross Jr. currently do most of the setup work for Farrell.
Though nearly all of the Red Sox's roster has turned over since Papelbon's departure, two of his closest friends when he was with the team still remain in Dustin Pedroia and David Ortiz.