Last week Cribbs and his representation went public after the Browns wouldn't budge from their $1.4 million per year offer. Cribbs made a base salary of $900,000 this past season and felt he was being low-balled. He has three years left on his current contract.
Holmgren Tuesday left the door open for further conversations with Cribbs. But "The Big Show" didn't seem too enthused that Cribbs is stating his case publicly.
"I'd rather that not happen," Holmgren said. "But we've been at this a long time. Is anyone surprised? That's just the way it is. I said what I said and I'll say it again: We as an organization will not negotiate in the press. We're not going to do that.
"But I love Josh Cribbs. So I'm hopeful things will work out and everyone is happy at the end of the day."
Cribbs made his second Pro Bowl after returning three kickoffs and one punt for touchdowns. The Browns finished 5-11 last season but won their last four games.
Cribbs cleaned his locker out last week and said it was "unlikely" he would return to the Browns.
"I did all the playing I'm going to play on this contract," Cribbs said. "I ain't doing nothing, I'm not showing my face until it's right."
Cribbs told The Plain Dealer of Cleveland he will request a trade, likely before the league resumes business after the Super Bowl on March 4.
"If they're definitely set on that offer, then I'm out of here, no question," he told the Cleveland newspaper.
"I'm not just insulted by the number, but by the fact they consider me just a kick returner," Cribbs told the paper. "I'm so much more than that."
He also rushed for 381 yards and had 20 receptions for the Browns (5-11).
James Walker covers the AFC North for ESPN.com. Information from The Associated Press was used in this report.