Murray's playing status has been uncertain since this past Monday, when he underwent surgery on his left hand. He told ESPN as recently as Saturday that he was still undecided on whether he would play.
"I have to do the right thing for myself, the right thing for the team," Murray said.
Murray's teammates are confident that he will play, and owner Jerry Jones said Friday that things were trending in a positive direction.
The NFL's leading rusher, Murray is officially listed as questionable on the injury report, and all involved agree that he would make the ultimate decision about whether to play a week after suffering a fracture in his left hand against the Eagles.
A protective plate and eight screws were inserted to facilitate healing and promote the quickest possible return to the field.
Murray has practiced wearing a glove he routinely wears but equipped with protective padding. Murray said he was involved in some contact in practice to allow him a sense of whether he could protect the ball, but acknowledged that is far different than playing in a game.
Murray's five lost fumbles are the most in the league among non-quarterbacks, but he has not fumbled in his past six games.
Murray said his decision would be based on pain tolerance and whether he is comfortable doing everything required of a running back.
The Cowboys (10-4) can clinch the NFC East title with a win Sunday, thanks to Philadelphia's upset loss Saturday to Washington.