The 26-year-old continues to be linked to a move to the Spanish side after another underwhelming season at Old Trafford that ended with the Red Devils finishing sixth in the Premier League.
Three years after United beat Madrid to the signing of the France midfielder, there is growing speculation that a switch to the Santiago Bernabeu is imminent this summer.
But his compatriot and ex-Arsenal player Pires says Pogba would be wrong to leave United at this point, insisting he still needs to establish himself as the leader of the team.
"My view about Paul Pogba is that he’s a great player, but I also know that last season especially was very difficult for him," he told The Mirror.
“A lot of people just talk about the transfer because Manchester United spent a lot of money.
“So maybe that was difficult for him to handle, particularly at the beginning. But for me, the most important thing is for him to continue at United.
“It is one of the best and biggest clubs in the world – and he has unfinished business.
“The reason United spent such a huge amount of money on him is that they believed a lot in Paul because he can be a real leader for their team.
“When the club spend a lot of money like this for you, it’s because they have faith in you.
“That’s why it’s very important to have this point in your head. I know Paul is very intelligent about this.
“They have invested a lot in him, so I believe it’s very important that he stays at United and delivers what
they know he can produce.”
"I know Madrid and Zidane want Paul and that may be hard for him to resist," he added.
"United will play in the Europa League next season and every player wants to play in the Champions League. Maybe Paul wants to win this competition with Madrid. But I think he has football to play in the Premier League."