A major transfer overhaul is expected at Old Trafford in the summer, with a host of both incomings and outgoings likely.
But Solskjaer will want to keep hold of his best players as he bids to revamp his struggling squad ahead of next season.
However, it looks like De Gea may be one of the stars heading for the exit door, as he struggles for form and confidence.
The shot-stopper has been chased by Real Madrid and PSG in the past – and the Sun claim United chiefs are bracing themselves for a transfer saga with the French giants in the coming months.
De Gea has been out of sorts lately, letting a tame Lionel Messi effort through his fingers at the Nou Camp, before being blamed for both goals conceded against Manchester City earlier this week.
The Sun report Solskjaer and his bosses are worried the Spaniard will be tempted by PSG’s £350,000-a-week wage offer, which is a figure United cannot match.
De Gea only has one more year to run on his Red Devils deal.
But it was recently revealed that United chiefs would rather let their No 1 leave on a free next season than lose him this summer for a hefty transfer fee.
The news regarding De Gea comes after:
De Gea is likely to remain in between the sticks for United until the end of the campaign.
But former Old Trafford goalkeeper Gary Bailey has called for Sergio Romero to replace him.
“De Gea has been an absolutely amazing keeper for United,” he tweeted.
“But perhaps time now to give him a rest and let him rediscover his mojo.
“We have a more than capable replacement in Argentinan international Sergio Romero !!”
United will be keen to bounce back to winning ways when they face top-four rivals Chelsea on Sunday afternoon.