United had travelled to Turkey in the second round of the Champions League.
The pair failed to break the deadlock throughout the 90 minutes, and as tensions boiled after the full-time whistle Eric Cantona was flashed the red card.
And when making his way down the tunnel, a Turkish police officer pushed him away from the pitch, leaving the Frenchman fuming.
Keane, speaking after the events, said it was the ‘only time’ he didn’t want to get involved.
Steve Bruce, who was also involved that day, said: “At the end of one tunnel was the sanctuary of our dressing room, but before we could reach it, I saw a policeman punch Eric Cantona in the back of the head.”
Before Keane added: “In the dressing room Eric went crazy. He was determined to go back outside to sort out the rogue cop who’d been wielding his truncheon.
“Eric was a big, strong lad. He was serious. He insisted he was going to kill ‘that f****r’.
“It took the combined efforts of the manager, (assistant) Brian Kidd and a few of the players to restrain him.
“Normally I wouldn’t have backed off a fight but even I wasn’t up for this one. There were a lot of Turks out there!”
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Cantona expanded on the incident in his book: “I was punched on the back of the head and it’s a great scandal.
“I just told him he was a bad referee.”
“What annoyed me most is that I was hit on the head with a truncheon by a policeman.
“The sort of fellow who sends you to prison for being out of work, or when you are hungry and you go and steal a bar of chocolate from the supermarket.”
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United players were ordered to not leave Cantona alone and to shower in pairs.
Cantona later added: “I had been hit from behind by that s*** of a Turkish policeman.
“Maybe we’ll bump into each other again some time!”