Pogba and Morrison were two of United's brightest academy talents, helping United lift the FA Youth Cup in 2011.
Speaking recently to the UTD podcast, Pogba revealed how he almost came to blows with Morrison during a training session at Carrington.
He said: "I have a nice story with Rav. A few weeks after I arrived, and now we're very good friends, but I will just tell you we almost fought – me and him.
"So I was training and obviously everyone knows how good Rav is with the ball. He was dribbling [past] players. I took the ball from him and he got angry a bit and kicked me.
"I couldn't speak English so I looked at him and [thought] 'that's OK, I'll wait until you get the ball [laughs]'. I smashed him.
"He started talking to me in English and I responded in French. You know, OK, we will see after in the changing room. OK, no problem. I'm not scared of you.
"After, he came to me and hugged, you know, and, since then we're very close. It's a strange story and funny but that happens a lot in football and now we're very good friends."
Barmby was present when the altercation occurred, which he says was only a 'bit of a scuffle'.
Such training stoushes were commonplace in an era at United when titles in one form or another were celebrated annually.
In the case of Pogba and Morrison, Barmby says it was simply about two players trying to assert themselves as the top man.
Asked about Pogba's story, the Phoenix Rising midfielder told Tribalfootball.com: "I actually think I was [there]. It was actually funny, people talk about this a lot, but in football there a lot of fights that the public don't see, because everyone is so competitive, and especially at that time at United, that was the culture, it was so competitive.
"I saw numerous scuffles on the training ground, but sometimes that's also healthy too because you kind of need that, and then all of a sudden you're fine again and everything is good. It was just one of them things.
"Them two were by far the best players and I think they were trying to see who was the more dominant alpha-male. I don't think there was much in it to be honest, a bit of a scuffle, but just two insanely talented people going at."
Surprisingly both players were touted for great things at United both left by 2012, but of course, Pogba returned from Juventus in 2016.
Meanwhile, Pogba collected the Europa League and League Cup in his first season back at the the Red Devils, as well as winning the World Cup with France in 2018.
Speaking about the Frenchman, Barmby added: "It doesn't come along very often.
"You see a lot of players that come through academies and they were maybe on the radar and all of a sudden they get through and burst onto the scene, but Pogba was the opposite you knew he was going to be a player, you knew he was going to reach the heights he is reaching now.
"He was by far the most talented player I've ever seen in my career."
Follow Andrew Maclean on Twitter: @andrewmaclean30