The pair clashed during their time at Newcastle United!
Indeed, Gillespie was shown up by the Newcastle legend after challenging him to take their differences outside.
Believe it or not, it all started with a bit of cutlery being knocked off a table...
And he told talkSPORT: "We were away on a mid-season break and I knocked some cutlery off the table accidentally. He looked over to say ‘pick that up’, and I just didn’t like the way he was talking to me.
"I just turned round and said: ‘Right. Outside now!’ And he took me up on the offer.
"I didn’t think he would but I was a bit too proud to back down. We ended up going outside, and I took one swing and missed, and he hit me - and that was goodnight."
Gillespie admitted the punch landed him in hospital because he had hit his head on a plant pot! But the former Newcastle man also said he and Shearer joked about the incident the following morning.
Interestingly, Shearer is well remembered by the Magpies faithful for another incident where he forwent the chance to be violent - against Roy Keane.
Indeed, the Manchester United hard man then provoked Shearer but he famously stood and watched as Keane got himself sent off.
Clearly, though, Shearer was a bit of a tough guy himself during his Newcastle days...