"I wouldn't sign a long-term deal there (with the Yankees). Those rules, that's old-school baseball," the left-handed pitcher said at spring training.
The Yankees' policy, put in place by owner George Steinbrenner when he bought the team in 1973, allows moustaches but forbids facial hair below the lip, and hair below the collar.
Plenty of Yankee acquisitions over the years, including Lou Pinella, Jason Giambi and Randy Johnson have traded their whiskers for Yankee paychecks and opportunities for championships, the New York Daily News said Thursday.
"Do you really think some player would say no, all things considered, it if was a good deal for them?" the Yankees' Derek Jeter said when hear of Price's comments.
At Tampa Bay, manager Joe Madden does not impose restrictions on facial hair, clubhouse music or attire on travel days, the newspaper noted.