Penn, 33, was taken to the hospital after the fight. It was his first appearance since he announced his retirement following a loss to Nick Diaz in October 2011.
White told ESPN.com he'd opt to see Penn hang up his gloves at this point. The former lightweight and welterweight champion has one win in his last six fights.
"I would love to see BJ Penn retire," White said. "I really do love the guy. All the good, the bad, the ugly we've been through over the last 13 years -- I care about him.
"He's got money. He's got a family that loves him. He's got a beautiful wife, kids, nothing left to prove. I would like to see BJ ride off into the sunset."
Penn's management team, when reached by ESPN.com on Saturday, declined comment.
Penn (16-9-2) is widely considered as one of the most talented mixed martial arts fighters of all time. He remains one of only two fighters to have won UFC titles in multiple weight classes. Randy Couture was the other.