The Chile international has spent the season on loan with Inter Milan after falling out of favour under Solskjaer.
However, the United manager said earlier this month that he is expecting Sanchez to "prove people wrong" when he returns from his spell at Inter in the summer.
According to the Manchester Evening News, though, Solskjaer has no real intention of integrating the ex-Arsenal star back into his plans.
Sanchez is under contract at Old Trafford until 2022 and it is claimed that United are seeking a club to pick up his £400,000-a-week wages from next season.
The 31-year-old started Inter's 4-2 win over bitter rivals AC Milan on Sunday and has featured 10 times for the Italian side in all competitions.