The World Cup-winning midfielder has been linked with Real Madrid and Juventus, although the Red Devils are adamant that Pogba won't be going anywhere, Daily Mail reported.
But according to The Sun, Pogba will sit down with Solskjaer once he returns from his holiday in the hope that he will be granted his wish to leave Old Trafford.
And the 26-year-old is hoping to leave the club before United's preseason tour gets underway in a fortnight's time.
The Frenchman remains unsettled in Manchester and earlier this month confessed it might be time for a new challenge away from Old Trafford.
Both Real and Juve are yet to make an offer for Pogba as of yet but they will need to fork out £150 million should United decide to sell.
Fellow Frenchman Zinedine Zidane, who was reappointed as Los Blancos boss last season, is reportedly keen on recruiting the midfielder despite splashing a staggering £344 million on five players already this summer.
Zidane is also eyeing up Ajax's Donny van de Beek should Real fail in the pursuit of Pogba.
Real's hopes of freeing up wages, however, look fairly bleak after Gareth Bale reportedly told the club he is planning on going on the preseason tour to America.
The Welshman's £650,000-a-week salary is proving a sticking point for Los Blancos, but Zidane will hope the club's top brass can loosen the purse strings once more to bankroll a move for the United midfielder.