Lingard was a second-half substitute in his side's 2-1 pre-season win over Derby County on Sunday.
It was his first appearance for the Red Devils since his prolific loan spell at West Ham last season.
Lingard's future has been the subject of intense transfer speculation, with the Hammers thought to be interested in signing him on a permanent deal.
But Solskjaer has other plans for the 28-year-old - saying he expects him at Old Trafford at the start of the 2020/21 campaign.
The Man United manager said: "He was one of the positives. He's a Manchester United player and he wants to fight for his place.
"He's come back bright, confident and with lots of energy. I think everyone saw what he did at the end of last season with West Ham.
"He's still in my plans. I expect him at Man Utd at the start of the season."
The star midfielder took to social media after featuring for Man United against Derby.
He tweeted: "We back. 45 in the tank and a solid win."
Lingard spent the second half of last season on loan at West Ham and starred under David Moyes, scoring nine and assisting five goals in 16 Premier League games.
Featured Image Credit: PA/Manchester United
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