Taillon told the Pittsburgh Tribune-Review that he's received that suggestion as a possible remedy.
"I said if it helps, I'll put a sign-up sheet and everyone can come and pee," he told the newspaper.
"I don't care. I just want (the cut) to go away."
Taillon was forced out of his last start Friday against the San Francisco Giants after three innings because of the injury.
Taillon wouldn't be the first baseball player to urinate on his hands as a form of treatment. Both Moises Alou and Jorge Posada, who both didn't wear batting gloves during their careers, have said they tried the practice to toughen up their skin. Los Angeles Dodgers pitcher Rich Hill said in 2016 that he urinated on his hand to try to heal blisters.
Taillon, who is 2-3 with a 4.08 ERA in eight starts, is scheduled to start Wednesday, but Pirates general manager Neal Huntington has indicated the team will be cautious with the right-hander.
"We'd rather err on the side of conservatism and have him miss one start than risk missing a couple because it doesn't heal properly," Huntington told reporters, according to the newspaper.
The Tribune-Review reported that Taillon currently is wearing a silver nitrate sleeve on the finger to try to speed up the healing process.