Lingard, 28, spent the second half of last season on loan at West Ham and was a revelation.
He scored nine goals in 16 Premier League appearances under David Moyes and won his place back in the England squad as a result.
The Hammers are just one of a host of teams who were linked with a permanent move for Lingard this summer but, speaking after a pre-season win at Derby, Solskjaer made it clear he wants to keep his man.
“He was one of the positives,” Solskjaer said. “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 Manchester United at the start of the season.”