Barry retired from mixed martial arts in 2013 but returned to his kickboxing roots to fight in the Glory World Series.
Saturday night he had a rough first-round knockout loss in Cincinnati.
"Brock Lesnar called me and begged me to make (Pat Barry) retire," White said.
"He said, 'I don't consider too many people my friend, and I consider Pat Barry a friend. Dana, you got to get this guy to retire,'" he added. "I said, 'Listen, he's a grown man Brock. What am I gonna do?' It's different with guys like Forrest (Griffin) and Chuck (Liddell), guys that I've had relationships with for a long time. Guys who have made a lot of money. That's the difference. You look at guys like Forrest. Forrest and Chuck are multimillionaires. It's easy to make them quit."
"It's a lot tougher to make a guy quit that has to make a living. I don't want to hurt Pat Barry or throw a monkey wrench in his life or anything, but at the end of the day, the state athletic commission is gonna need to step in and help a guy like Pat Barry retire... or people that care about him," White said.