Since his loan move to West Ham United in January, Lingard has been one of the most prolific players in the Premier League.
The 28-year-old has eight goals in nine Premier League starts for the Hammers.
Scholes believes that manager Ole Gunnar Solskjaer should welcome Lingard back into the fold for next season.
"He'd had a tough time at United and I think that was all from bringing Bruno Fernandes in," Scholes told talkSport.
"They are players in similiar positions and you couldn't argue with what Bruno has done.
"Jesse needed to play football – he needed a chance – and West Ham gave him that chance.
"I know the quality Jesse has. I worked with Jesse as an 18/19 year-old as a coach so I know the quality he possesses.
"His fitness was never going to be a problem even though he hadn't played for a while, he's so professional and so fit.
"He's been sensational. For Ole, I think it would be great to have him back to give some competition to Bruno Fernandes.
"When he isn't quite doing it we have a player in Jesse Lingard who is capable of reaching the same heights.
"His numbers since he's been at West Ham have been just as good as Bruno, so it's always healthy to have competition in the squad.
"Hopefully Jesse is ready for that and Ole wants him to do that as well."