According to Joel Sherman of the New York Post, Papelbon has told the Phillies he will only waive his no-trade clause if he will be the closer on his new team.
Papelbon, 33, has 25 saves this season and a 1.83 ERA in 44 appearances. He has blown just three save opportunities.
The Phillies are in last place in the NL East with a 46-59 record through July 27.
Speculation that the Phillies might try to move Papelbon began as early as last winter.
Papelbon is making $13 million this season and is due to make the same next season. He has a vesting option for 2016 worth another $13 million.
- Dan Gartland