Despite their clash of personalities, Cole and Sheringham showed you didn't have to like your teammates to play well together, which they did at Manchester United.
The animosity had begun, in Cole's mind, in 1995 when he was making his England debut and was replacing Sheringham against Uruguay.
"For all the respect I had for him, he was far from pleased to see his number come up and instead of greeting me on the sideline to wish me luck or congratulate me, he dejectedly walked off, 25 yards down the touchline, without looking at me, or acknowledging my moment," he wrote in new book Fast Forward: The Autobiography: The Hard Road to Football Success.
His special moment was ruined and he never forgave Sheringham.
Cole was an established Man United player when Sheringham was signed in 1997 from Tottenham where he join forces once again with Roy Keane, whom he had shared a changing room with at Nottingham Forest in the early 90s.
And in his book, which is serialised in The Times, Cole recalled a 1-1 draw with Bolton at Old Trafford in 1998 where his fellow striker turned to him as they walked up the tunnel and told him Bolton's goal was his fault.
"What? I scored the equaliser, and now he's saying that," he wrote.
"I run up the tunnel and just as he gets to the dressing room, I'm ready to steam in. I'm screaming all sorts and trying to throw punches, but everyone's on me, pulling us apart.
"The next thing I know, Roy Keane has me up against the wall and he's shouting in my face. 'What the **** are you doing, Coley? Sort yourself out. We're a team.'
"I'm not hearing him, but I calm down, and suddenly Roy is going for Teddy, ripping into him, and it's our turn to try to pull them apart. 'What's all that about, Skip?' I ask a clearly incensed Keane. 'You wanting to fight him reminded me of what a ***** he was to me at Nottingham Forest!'"
They were told off by Sir Alex Ferguson, though they Cole and Sheringham never got over their personal dislike.
Keane, meanwhile, has put on record he never fully got on with Sheringham in their two stints at club level together and wrote in his own book about his first day as a United player.
"Teddy arrived for training on his first day at the club in his red Ferrari, every inch the confident Londoner.
"Teddy and I were acquainted from our Forest days but the chemistry between us was never quite right."
It clearly never had any impact on the pitch, though, as all three were part of the 1999 treble winning season in what was a hugely successful period for the club.
Andy Cole and Teddy Sheringham never saw eye-to-eye and, according to Cole, Roy Keane wasn't fond of the striker either.