The Chilean is said to be "deeply disillusioned" with life at United, and his representatives are "sounding out potential clubs," according to John Cross at the Mirror.
The Red Devils are "willing to cut their losses," on Sanchez who only arrived at the club in January from Arsenal and has a contract worth over £500,000 a week, per the report.
Sanchez has failed to consistently produce his best form since moving to Old Trafford. He has managed only one goal so far this season and has been left out by manager Jose Mourinho in recent weeks.
The forward also missed the UEFA Champions League defeat due to a groin injury, according to Fox Sports Latin America (h/t Metro).
The 29-year-old was seen as something of a coup when he signed. However, he has failed to provide the goals, assists and creative verve that made him such a success at Arsenal.
Sanchez's first goal of the season came against Newcastle United when he came off the bench to score the winner in a 3-2 victory. It also ended a long goal drought:
Former Arsenal star Robert Pires has offered his verdict on Sanchez's situation and hinted he could move in the winter transfer window, per El Mercurio (h/t Lucas Sposito at Sport Witness).
"Sanchez doesn’t deserve to be on the bench or stay at home," he said. "We’ll see if he finds a solution in January, because he is not playing and he has to do it, since he is a wonderful footballer."
PSG were interested in signing Sanchez before he left Arsenal and moved to Manchester United, per Cross.
Yet the French champions already boast a formidable attack consisting of Kylian Mbappe, Neymar and Edinson Cavani.
The trio have already guided PSG to the top of the Ligue 1 table, where they are eight points clear of Lille. Thomas Tuchel's side have scored 37 goals in 10 games and are hardly lacking in firepower.
Sanchez's enormous wages may also provide a stumbling block. Few clubs in Europe will be able to afford to match his salary, particularly with the Chilean also struggling for form.
In the meantime, Manchester United will be hoping he can rediscover his goalscoring touch, and he may get a chance if Mourinho decides to drop Romelu Lukaku.
The Belgian is without a goal in his last eight Manchester United appearances, and Mourinho could opt to take him out of the team and bring in Sanchez in a central role.