The France international has been heavily linked with a move to La Liga giants Real Madrid over the past couple of weeks.
Reports in England have suggested that Pogba was prepared to force a move to the 13-time Champions League holders.
Real Madrid boss Zinedine Zindane is thought to be eager to sign Pogba to bolster his options in the middle of the park.
Juventus have also been touted with an interest in re-signing the 26-year-old before the start of the new Premier League season.
Pogba has spent three seasons at Old Trafford but the versatile midfielder has struggled to live up to his £89m price tag.
Former Arsenal and France midfielder Pires believes that Pogba should stay at Manchester United.
“Paul Pogba has football to play in the Premier League,” Pires is quoted as saying by The Sun.
“I know this season especially was very difficult. A lot of people talk about just the transfer because Man United spent a lot of money. Maybe that was difficult for him.
“I know Madrid and Zidane want Paul Pogba but, for me, the most important thing is to continue at Manchester United. It is one of the best clubs in the world.”
The Sun go on to add that Manchester United will look to secure a £150m transfer fee for the World Cup winner.
Pogba has won the Europa League and the League Cup since his return to Manchester United in 2016.
The French star scored 13 goals and made nine assists in the Premier League last season.
Manchester United finished in sixth place in the Premier League table last term to miss out on a Champions League spot.
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