Lingard will be welcomed back at United following his prolific loan stint at West Ham, according to Solskjaer.
“Jesse has been brilliant since he left and I've answered this quite a few times," the Norwegian said at a press conference held before Thursday's Europa League quarter-final second leg against Granada at Old Trafford.
“Selfishly we could have kept him because he's always got a part to play.
“Jesse is a fantastic lad around the place, Man United through and through, never once did he moan or cause me a problem.
“He just came in, worked really hard and deserved a chance to play more football. That's why we let him go to West Ham, because he deserved a chance for what he's done throughout his life at Man United.
“Of course we welcome him back. I hope he will go to the Euros, because with his performances now and the confidence he's got, I don't think that's beyond him.
“I hope he's got a strong finish to the league. It was different here, the form Bruno [Fernandes] has played in arguably in Jesse's favoured position.
“That was just a decison that we made. Delighted though for Jesse and wish him all the best for the rest of the season until he comes back."