The Browns have been less than pleased with their running backs during training camp, and coach Mike Pettine acknowledged that Ray Rice's name has come up in discussion.

BEREA, Ohio—No critical mass has been reached in Cleveland’s backfield just yet, but with the Browns clearly dissatisfied with their young rushers early this preseason, file away the Browns as one of the more logical and likely landing spots for former Baltimore running back Ray Rice.

Browns coach Mike Pettine acknowledged to SI.com Tuesday that the club has discussed signing Rice, who has been out of the league since being released by Baltimore last September, the day the infamous elevator surveillance camera footage of his attack on his then fiancee surfaced.

Pettine was asked if the Browns were considering adding a veteran to the mix at running back, to go with second-year players Isaiah Crowell and Terrance West and rookie third-round pick Duke Johnson. “We’ve talked about it, but I don’t think we’re there at this point,” Pettine said.

Could that veteran be Rice? Pettine was quick to point out the ties he and at least one member of his coaching staff have with Rice.

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“Of course it’s a natural question here because of [Browns running backs coach] Wilbert [Montgomery], and because I was with Ray when he was a Ravens rookie (in 2008) and know a lot of people in Baltimore,” Pettine said. “Obviously Wilbert was his position coach for Ray’s first six years in the league (2008–13). I’m not going to say it didn’t come up in discussion, but at this point we’re not there yet.”

Rice never played in Baltimore for any other running backs coach but Montgomery, unless you count the 2014 preseason, just before his career went into hibernation. Under Montgomery, Rice earned three Pro Bowl berths, and topped more than 1,100 rushing yards and 1,600 yards from scrimmage in four consecutive seasons (2009–12). His 9,214 yards from scrimmage in '08–13 ranked fourth overall in the NFL in that span. In addition, Pettine served as the Ravens’ outside linebackers coach in 2008, before leaving for a job on Rex Ryan’s staff with the Jets the following year.

Rice, 28, continues to generate little or no interest on the NFL’s free-agent market, in part because he had the worst season of his career in 2013 (the most recent season he played), averaging just 3.1 yard per carry and rushing for just 660 yards, and in part because of how radioactive his name became as the face of the league’s domestic violence problem. The running-back needy Cardinals reportedly offered another veteran free-agent rusher, ex-Jets and Titans star Chris Johnson, a one-year deal on Tuesday, but Rice still remains a man without a team.

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Asked if Rice’s recent controversial past would preclude him from being signed in Cleveland, or whether anyone in the Browns organization viewed him as untouchable because of the potential for a public backlash to his arrival, Pettine said his club would deal with that question only when the need for a veteran runner became pressing enough.

“I don’t think it’s gotten to that point, to say, ‘Hey, I’d kind of be comfortable with it,’” Pettine said. “But I think it would get to that point if we arrived at it from a football standpoint, then asked that question. Instead of working the process backwards. Why bother with asking the question if the need never presents itself?”

Perhaps the first game or two of the Browns preseason schedule will help determine the level of need in the backfield, one way or another.

In Browns camp on Aug. 9, Montgomery pulled few punches in critiquing the first two weeks of work turned in by his top three running backs, bemoaning that no one had seized the lead in the competition for the No. 1 job—“Nobody wants the role”—and labeling it “a total setback” that some of his backs had reported to camp in less than top condition. Montgomery also reminded his group that running backs have to play through pain and injuries at times.

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West missed time last week with a calf strain, returning to practice over the weekend, while Johnson has battled a lingering hamstring problem that cost him the Browns’ intrasquad scrimmage on Saturday in Columbus, and will sideline him for Cleveland’s preseason opener against visiting Washington on Thursday. In addition, Crowell, last year’s second-leading rusher for the Browns with 603 yards, has yet to distance himself from the pack, and the whole picture in the backfield has been troubling for a team that hopes to build its offense around a strong and consistent running game.

Pettine called the fact that his top three running backs didn’t report to camp in great condition “disappointing,” adding “it was Duke as well. It was the three of them. That’s a tough deal to have, three guys in that room and they struggled. They struggled early and two of them obviously got hurt.”

Montgomery’s unvarnished message-sending had the full blessing of his boss, the Browns second-year head coach. “I don’t want my assistants saying anything publicly that they wouldn’t tell the player to his face,” Pettine said. “But Wilbert’s old-school, blunt force trauma, however you want to categorize it. That’s Wilbert. I had no issue with that. Those young guys, sometimes they need a bucket of cold water thrown in their face, and Wilbert’s just the man for the job.”