"Obviously I think they want me here," Murray said Tuesday night at a promotional event. "I want to be here. It's just finding the ... just what helps them, what helps me. Things like that. I think both sides want to be here, so I think we'll see where it goes."
Murray would not say whether there have been ongoing negotiations between his agent and the Cowboys.
Since the Cowboys' season ended, he has attempted to relax and enjoy the fruits of a season in which he led the NFL in rushing with 1,845 yards and was named an All-Pro and the NFL offensive player of the year.
Murray said he would be involved in the talks with the Cowboys or other teams should he not re-sign before free agency begins.
"I'm very patient so ... if that's the process I have to go through, then that's the process I have to go through," Murray said.
Murray figures to be one of the free-agent prizes after such a strong season, but teams have shied away from making big financial commitments to running backs in recent years.
"At the end of the day, it's all about respect, and I think different people show their appreciation in different ways," Murray said. "I don't need a pat on the back. I don't need someone telling me how good I am on a constant basis and whatnot like that. I understand my value, so to speak, and I understand what I bring to the table."
Murray has not distanced himself from the Cowboys since the season ended. Last week he attended the Cincinnati-SMU basketball game. He did not view his time with Jason Garrett and Tony Romo as a recruiting pitch by the coach and quarterback.
"Those are my guys," Murray said. "Like I said, I made it clear to everyone if I'm not here next year, Romo will be my guy, [Jason Witten] will be my guy, [Dez Bryant] will be my guy. Jason will always be a great [friend]. The Joneses will always be great friends. Just great people in my life. There's no hard feelings."
Murray reiterated what he said at the Pro Bowl: His final decision will not be solely about money.
"It's about winning a Super Bowl," Murray said. "If this place gives me the best chance, I'm going to stay here."