Lingard impressed on his return to the team following a loan spell at West Ham United after playing the second half in a 2-1 win over Derby County at Pride Park on Sunday.
The 28-year-old left Old Trafford in January to find regular first-team football but Solskjaer insists he wants to keep the England forward after finding himself short of options at the end of last season.
"Jesse has come back, been bright, he wants to fight for his place and there's nothing better than seeing players want to fight for their place," Solskjaer said.
"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."
Dean Henderson is back in training after pulling out of the England squad with a hip injury while David De Gea is still on holiday but Solskjaer is not expecting Heaton, 35 to be content with being third choice next season.
"Tom was very positive," Solskjaer said. "He's here to give the other ones a bit of a challenge as well. He's conducted himself so well throughout his career and I was just at the end of my career when he was coming up. I'm so happy we have him.
"Tom wants to play. He's been unlucky with the injury last season and I think he would have been in the England squad if not. He's got those ambitions."
Solskjaer has revealed it's only "paperwork" which has prevented United from announcing the €85m capture of Jadon Sancho from Borussia Dortmund while he also expects Facundo Pellistri, a scorer against Derby, to go out on loan again after spending the second half of last season at Alaves.
"They're not ready yet," Solskjaer said. "They'll probably be 100% training with us a week on Monday. They're still working hard to step into the group."
Solskjaer added that United are monitoring the situation regarding Marcus Rashford's injury.
Sources told ESPN last week the club hope the striker will recover from shoulder surgery in time to feature in a crucial run of fixtures at the end of October.
"No, we're looking at the best options," Solskjaer said. "Of course, he went away just to reflect on it a little bit. We have to take the best course of action for him and the club.
"We're still addressing that with the experts."