Team officials have said the trade centered around sending Murphy to Philadelphia for relief pitcher Jeff Parrett.
But the Atlanta Constitution said in today's editions that the Phillies have balked at the Braves' demand for another, unidentified player in the package.
Braves General Manager Bobby Cox refused to comment.
As a 10-year veteran Murphy had the right to veto a trade, but he will not do so, his agent, Bruce Church, said Thursday.
"Where it goes past here is up to Bobby," Church said. "I guess you could say we're waiting on him."
If the Braves grant permission, the Phillies could begin contract talks with Murphy, whose pact expires at the end of this season.