Murray, officially listed as a limited participant on the practice report, went through individual and team drills Thursday and said his surgically repaired left hand felt good.
"I'm a very competitive person and I want to help this team out as much I can, so whatever that portrays me doing Sunday, then we'll see," Murray said. "But I've had two good days, and we'll see how it goes."
Murray had surgery Monday night to insert a plate and screws to stabilize a broken fourth metacarpal in his left hand. He has worn a hard plastic shell on the top of his glove for added protection during practice.
The Cowboys (10-4) lead the NFC East, and a win over the Colts would maintain their division lead over the Philadelphia Eagles. With a loss, the Cowboys likely would need other teams to lose in Week 17 to make the postseason.
"Even though we're at home, we shouldn't leave anything back at the house," owner and general manager Jerry Jones said. "We've got to put it all out there. If he can help us win, then that's the smart decision as far as strategy is concerned.
"As it turns out, this isn't about strategy; this is about him. But I do think that his attitude about it is inspiring for everybody."
Had Murray suffered this injury earlier in the season, perhaps his willingness to play would be different. In 1999, Emmitt Smith had a similar surgery halfway through the season and missed a game. In 2006, Terrell Owens did not miss a game after having the same surgery because the Cowboys had a bye week.
"I think it's all about with every player on our team: Can I play this week?" coach Jason Garrett said. "These games are valuable. You get 16 opportunities. Our players are competitors. They want to play. They understand the importance of playing, not only for themselves but maybe more importantly for the team and the accountability they have to each other.
"That's really Line 1: the passion, the desire to play, and he certainly has that. So he's going to do everything he can -- just like we would with any of our players to try to get them ready to go."
Garrett and Jones said they have been told by the team's medical staff that Murray's hand is no more at risk Sunday than if he decides to sit out a week.
"Whenever you talk to the doctors or you talk to these trainers, when they get right down to it, they say, 'Well, the player has to tell us if he feels like playing or not,'" Jones said. "I'm glad to know that there's not a lot of risk of extending the injury time or exacerbating the injury, which is a good thing. That means if he can feel comfortable and tolerate and execute, then he'll play."