Manchester United No 1. De Gea has been heavily linked with a move to PSG after stalling over a new deal.
The Spaniard wants to earn around £350,000-a-week in wages at Old Trafford, with Solskjaer keen to sell any player that isn’t devoted to the cause.
According to The Sun, De Gea must decide by the end of next week if he’s committed to United.
De Gea’s high standards have dropped in recent weeks with high profile mistakes against Chelsea and Barcelona amongst others.
Although Solskjaer has confirmed that De Gea will keep his place for their clash against Huddersfield on Sunday, pressure from Sergio Romeo and interest in Real Madrid stopper Keylor Navas leaves his postion in doubt.
“David’s been training well this week and he will play,” Solskjaer said.
“David has been fantastic this season.
“Towards the end he’s been in headlines for the wrong reasons but he has to deal with that.
“The goalkeeping department has experienced better times than just now but David is ready for Sunday.
“David’s confident and looking forward to the next two games, he wants to prove how good a goalkeeper he is.
“The performances over the years, David’s got all my confidence.”
De Gea’s contract runs out next summer and United run the risk of losing him on a free if he remains without signing a new deal.
His future could depend on the club’s ability to win trophies in the near future, and also on whether they reach next year’s Champions League.
Solskjaer added: ”In long-term planning we have to think about being in the Champions League next year and the fact we might not be.
“You would be surprised how many players’ agents have been telling us their players would love to be a part of Manchester United in the future.
“That is the lure and the potential and size of the club and we will get back to the good days.”