The Spain international has less than 12 months left to run on his current deal at the 20-time English champions.
Manchester United could risk losing their number one goalkeeper for nothing unless they can reach an agreement with one of their longest-serving players at the club.
Reports in England suggested this week that De Gea will commit to a new deal with the Red Devils when the club return from their pre-season tour of Australia next week.
Speaking at his media conference on Tuesday ahead of Manchester United’s clash against Leeds United at Optus Stadium on Wednesday, Solskjaer provided an update on De Gea’s future.
“He’ll play tomorrow and hopefully we can agree with David,” Solskjaer said. “As I’ve said a few times, that’ll be up to David and the club to announce if that happens, if and when.”
De Gea is set to start his first game of the 2019-20 season when Manchester United take on Leeds in their pre-season friendly in mid-week.
Manchester United have already signed two new players in the summer transfer window as Solskjaer looks to improve his squad ahead of the new season.
Swansea City midfielder Daniel James completed an £18m move to Manchester United in June before Crystal Palace defender Aaron Wan-Bissaka secured a £50m switch to the Old Trafford outfit following weeks of speculation.
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