Cole had been signed by Souness from United for £8million in 2001, and enjoyed a decent start to his spell at the club.
But their relationship soon became fractured, with Cole eventually reporting Souness to the PFA for unfair treatment.
“My issue with Graeme was back then, Graeme was a bully,” Cole told The Beautiful Game Podcast. “And I was basically saying to Graeme ‘it doesn’t work like that, I have grown up different. Bullying don’t work’.”
“I took up a challenge against a man I really held no fear to. Graeme is old-fashioned, he’s very old-fashioned and he’s very set in his way.
“He was an unbelievable midfield player back in his day, but when a man is set in his way with the way he used to play and the way his team-mates used to play, he looks at the game totally different to what it is now. And that is him.”
Souness has long stepped out of the dugout and into the TV studio, but is now often heard attacking current United star Pogba, with the player’s attitude and work ethic frequently called into question.
Rio Ferdinand has recently defended Pogba from Souness’ criticism, and Cole has now weighed in on his old boss.
“When he talks about Pogba, I get frustrated,” Cole said. “I am one of Paul Pogba’s biggest fans and when people constantly have a go at him, I am disappointed.
“Yeah he hasn’t played as well as he would have liked but a man won’t win the World Cup unless he can play the game. He’s got every attribute.
“I hope he stays at United for many years to come and proves to individuals who speak about him in that tone what he is all about. He is a quality player and whatever Graeme has got against Paul, only Graeme can answer that question.
“Not every player can play like Graeme Souness but not every player can play like Pogba.”
Sign up to the Mirror Football email here for the latest news and transfer gossip.