Manchester United star Sanchez has failed to sparkle since Solskjaer replaced Jose Mourinho in December, finding the net just once in the time since.
That came in a 3-1 FA Cup win over Arsenal in January where he looked one of the best players on the pitch.
But Sanchez has struggled for Manchester United ever since and is facing a spell in the reserves following a clash with youngster Mason Greenwood in training.
And the Times say the Chile international now wants to leave the club – and is hurt by Solskjaer’s decision to sell Lukaku.
The duo were close at Old Trafford.
But, on transfer deadline day, Lukaku was allowed to leave for Inter Milan in a huge £73million deal.
Sanchez’s best games for United were often when he was in the same side as the Belgium international.
And with his close friend no longer at the club Sanchez himself is eager to pursue a new challenge somewhere else.
That may involve a compromise involving either the player or United to make that happen.
The Red Devils have been trying to offload him all summer long but, due to his high wages, have been unable to find a buyer.
United may have to pay part, or all, of Sanchez’s salary just to get rid of him.
Either that, or the player himself takes a pay cut in order to escape his Old Trafford hell.
Meanwhile, former United star Robin van Persie recently opened up on Sanchez and explained his issues since joining from Arsenal in January 2018.
“He doesn’t look very happy to me,” said Van Persie.
“He looked happy at Arsenal. He doesn’t look happy now.
“What I’ve seen and felt over the years is that how you feel mentally, how your life is, has a big influence.
“If you’re happy, you’re 50 per cent fitter, you create more and you enjoy yourself.
“So he should find a way mentally to change that.”