De Gea’s current contract expires at the end of the 2019/2020 season but the Spanish goalkeeper is yet to agree terms on a new deal.
Discussions with the Manchester United hierarchy over a new contract have been held for some time but an agreement is nowhere near in sight, leaving De Gea’s future uncertain.
Manchester United risk losing De Gea for free next summer if they are unable to coax him into signing a new deal but manager Solskjaer is adamant his first choice goalkeeper will soon put pen-to-paper at Old Trafford.
"I'm positive, of course, with David. I've said many times how lucky I am and happy we are to have him in goal," Solskjaer told reporters in Perth ahead of Saturday's friendly with Perth Glory.
"David has had a close-season where he has been negotiating and we hope we can get it sorted. I am positive. We hope he stays here for many years."
Only a faulty fax machine prevented De Gea from joining Real Madrid on transfer deadline day in August 2015, after an agreement worth £29m plus Keylor Navas had been agreed between the Red Devils and Los Blancos.
De Gea joined Manchester United from Atletico Madrid in 2011 and he has won Manchester United’s player of the year four times in the last six seasons.
De Gea had a difficult time between the sticks towards the end of the 2018/2019 season but he still remains one of the best players in his position worldwide.