Shearer joined the Match Of The Day host and Micah Richards on The Rest Is Football podcast when he was asked about the funniest thing that someone said to him on the pitch.
The Newcastle United legend replied: "Roy Keane once said that he was going to knock me out."
Lineker replied: "You do surprise me, and did he," to which Shearer laughed: "Come on!"
However Lineker had his colleagues back, saying: "I think I'd back you against him, Al. Even now.
"I think that people would pay to see that. You get all of these celebrity fights now - get the two of you in UFC gloves or boxing gloves…"
READ MORE ON ROY KEANE
Ex-Liverpool man once told Keane 'you can't take your medals down the pub' in long feud
Footage appears to show Keane call Ronaldo a 'w*****' and 'p****' during Man United game
However, Shearer was having none of it as he replied: "I wouldn't. I'm too old for that s***, Gaz!"
Posing the same question to Micah Richards, the ex-Man City replied: "No one was messing with big Mics on the pitch! They were terrified of me.
"The only encounters I had were with Ashley Williams and Clint Dempsey.
"Back in the day, he was at Fulham and I was at Man City. He was playing sort of left wing and I was at right back and I was quite small then, but I had a great leap and I kept winning the ball over him.
Most read in Football
How Sir Jim Ratcliffe's ownership could cost Man United a place in the Champions League
Man United on brink of £110m financial black hole as Sir Jim Ratcliffe nears takeover
FA to review Defoe transfer to Portsmouth which could lead to major sanctions for Spurs
Manchester United mocked by Checkatrade with not-so-subtle advert next to Old Trafford
"He was just getting frustrated and one of the times I won the ball and he shrugged me like 'what are you doing'.
"So me being from Chapeltown, I wasn't having that - there was no chance I was having that!
"I said f*** off and it went back and forth and then he turned to me and said: "You don't know where I'm from, dawg!
"I just thought, 'what are you even on about'. It keeps bubbling on because you think 'next time I see him he's getting it' but around that time people did a bit of research and found that he's a pretend rapper.
"So the next time I see him, I said 'f*** me, you can't even rap' and I just laid into him, saying: 'who do you think you are, Eminem?'
"I was singing Slim Shady throughout the whole game!"