Lingard having struggled for game time after the arrival of Portuguese midfielder Bruno Fernandes was loaned to West Ham United in the second-half of last season.
The 28-year-old had a successful loan spell with the London-based club and has returned to United after the stint.
With respect to his magnificent performances with the Hammers, Solskjaer has no idea of letting him move away from the Old Trafford as they prepare for a competitive side going into the new season.
"He was one of the positives. He’s a Manchester United player and he wants to fight for his place,” said Solskjaer after the game.
“He’s come back bright, confident, and with lots of energy. What he did towards the end of last season, that’s the true Jesse, that’s what we know he’s capable of and I think we saw towards the end that we lacked some options at times and Jesse is in the plans at the moment, yeah.
"He’s still in my plans. I expect him at Manchester United at the start of the season,” Solskjaer stated.
Solskjaer's declaration of Lingard's future means West Ham's chase of making his deal permanent would be impossible.
The loan move for Lingard was somewhat a blessing in disguise as that turned him into a goalscoring figure for David Moyes' side, scoring 9 goals in sixteen appearances.
Lingard came off the bench in the second-half in United's 2-1 pre-season victory over Derby County with goals from Tahith Chong and Facundo Pellistri.
The last season's runners-up of the Premier League will be a firehouse in attack with the return of a much more confident Lingard back on the roster.