"He just wants us to look professional, nothing unkempt. Just keep it clean," Reds reliever J.J. Hoover said.
Price sensed that people were talking about the rule when he met with reporters on Saturday morning.
"Should we talk about the beard?" Price said. "I think every year, you re-invest some time in your policies. We're going to spend some time with our core group of more established players and really talk about what we feel is important, not just from my perspective, but from a team and organizational perspective. I don't think you're going to be terribly successful if you sit there and turn back the clock on the clubhouse too far. I believe in our initial policy that facial hair is fine, but just keep it under control."
Price said the suggestion for trimmed beards did not come from ownership. There will be discussion of other team rules in a meeting once the full squad reports on Wednesday.
"There will be certain things I feel adamant about and some things we should talk about collectively," Price said. "In the end, if you have policies that guys don't buy into in the clubhouse, you're going to spend way more time than you want trying to enforce things that guys just don't agree with. I don't think there is anybody in there that's looking to turn this place into Fantasy Island and go crazy in there. Everybody wants to understand what the rules are and where the lines are drawn."
Hoover and fellow relievers Sam LeCure, Logan Ondrusek and Curtis Partch had beards last season. Hoover's was particularly burly and long.
"It doesn't matter to me. It's just a beard. It's just hair," Hoover said. "I'm happy I don't have to go clean shaven every day. It's fine."
One player who is popular, in part, because of his big, bushy mustache is catcher Corky Miller. Is his facial hair safe?
"Corky is going to be just fine," Price said.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.