The Irishman, who works as Paul Lambert's assistant manager at Aston Villa, suggested in his new autobiography The Second Half that Vieira would have beaten him in a punch-up.
"I haven't read it, but I have heard a lot about it," ESPN quotes Vieira as saying. "If there was a fight, it would take a long time to beat him and I would end up with a few cuts. I don't think he would give up easily!
"I'm not surprised at all about how honest he has been in the book. That's because the way he wrote the book is the way he was as a player. He's not the kind of person to go halfway. He's either everything or nothing. I think the book is him."
Keane, who highly criticised former United manager Sir Alex Ferguson in his book, released the autobiography last week.