The 26-year-old ran over 1,000 yards for the first time in his three-year career in the 2013 season, and believes that he is ready to take on more responsibility to ease the pressure on Tony Romo, should the team ask him to.
Murray told Fox Sports: "If they decide to do that with me, of course. Whatever they decide to do with me, I think I can handle it.
"You just have to take care of your body and know when to go and fight for that extra yard or inch and know when not to.
"That's something about just being a smarter football player in general and knowing when you're helping your team and when you're hurting your team."
Murray had a total of 1,474 yards from scrimmage and 10 touchdowns last season.