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CLEVELAND, Ohio -- The Browns would like to re-sign running back Peyton Hillis, who worked his way back into the team's good graces over the final six weeks of the season, a league source said.

Hillis, who becomes an unrestricted free agent March 13, showed the Browns enough over the final six games -- both on and off the field -- that they'd like to have him back at the right price. The Browns can re-sign their own free agents at any time.

General Manager Tom Heckert said at the end of the season that the Browns would talk to the agents for all of their free agents and hoped to re-sign some. He cited D'Qwell Jackson and kicker Phil Dawson as two the Browns would pursue.

But Hillis made his way onto that list down the stretch, including a 112-yard rushing performance against the Ravens on Dec. 24, averaging 4.7 yards on his 24 carries during a 20-14 loss.

A day after the season ended, Browns coach Pat Shurmur said, "I'll tell you what, Peyton and I had a great conversation yesterday. He's an all-star player who was dealing with injury in the middle part of the year and then came back, and I really liked what he did at the end of the season."

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After recovering from a hamstring injury that caused him to miss five games in the middle of the season, Hillis rushed 101 times for 376 yards over the final six games, including a 99-yard game in Arizona. He averaged 62.6 yards during that span, which projects to 1,002 yards over a 16-game season.

Hillis made his thoughts clear the week after that Ravens game.

"I'm a Cleveland Brown at heart," he said. "Since I've been here, I fell in love with the fans and the city and the people that live here. They've been nothing but 100 percent supportive through everything when I talk to them. And it's good to have a second family backing me like that."

The Browns are not believed to have had any contact with Hillis' agent, Kennard McGuire, since midway through the season, but are expected to contact most of the agents over the next month or so.

In November, around the time the Browns' leadership group met with Hillis to help him get re-focused, the Browns had all but decided to let him walk in free agency. By then, he had endured his strep throat incident and had gone back to Arkansas at midweek to get married instead of receiving treatment to try to play with the hamstring injury.

But Hillis settled down off the field and played well on it. Whether or not they can agree to a deal remains to be seen, but the Browns are more open to it now.

On Twitter: @marykaycabot