Murray, a physical back who often looks for contact, rarely leads with his helmet but says there could be instances where he comes face-to-face with a defender trying to bring him down.
"I'm not changing my running style," Murray said last week at a charity event. "If I get fined, hopefully, [Tony] Romo will take care of the first couple [of fines]."
Earlier this offseason, Cowboys coach Jason Garrett said he had concerns about how the NFL will regulate the rule.
"It's really a tricky thing from the standpoint of, it's so well-intended," Garrett said. "We all understand the challenges that it puts the officials in. A lot of the defenseless player calls they've had to make over the last couple years are hard calls. The game happens fast, and they've got to be bang, 'He hit him with his head first; it wasn't his shoulder.' Players duck. All the things that go into making those snap judgments. They're difficult.
"I think the real concern that the coaches might have is simply that it's a hard rule to officiate, and far be it from us to say we understand what an official's going through. But the game does happen fast and those collisions happen quickly. I think it's well-intended."
The Cowboys said they are working with Murray to keep his head up.
"We've talked about it," running backs coach Gary Brown said. "We are going to have a plan to try to get better than that. He's explosive enough that he can freeze people's feet and get away from them and do the things he needs to do to gain more yards.
"What is going to happen is he's going to be better because he will be able to see. He will have to keep his eyes up, his head up. ... We want them to be safe. We want them after their careers are done to be able to play with their children and things like that. So it is a bigger picture. It's for their future.
"If you keep your head up, you can see what's going on. If you drop your head, you are going to break your neck eventually."
Durability has become an issue for Murray. He missed six games last season due to a sprained foot and three more games his rookie season, 2011, with a fractured ankle.
Cowboys officials, concerned about Murray's health, drafted Oklahoma State running back Joseph Randle in the fifth round as insurance.
"You can just coach him hard and try to encourage him and try to just make sure he's doing the right thing to take care of his body because a lot of those injuries are freak things," Brown said of Murray's health. "Nothing we can do about it. He just has to be blessed with a 16-game season and hopefully that will happen."
Of course, if Murray gets fined for leading with his helmet, Romo's new $108 million deal, should be more than enough to pay for it.