According to Miguel Delaney at The Independent, PSG are one of the few clubs who could afford the Chilean's £500,000 a week wages, but they "don't feel it is worth moving for a player who is already 29 and has been struggling for form."
Sanchez regrets joining the Red Devils and had "explored the possibility of a deal with PSG," but he is expected to remain at Old Trafford, per the report.
Sanchez has struggled for form since joining Jose Mourinho's side from Arsenal in January. He's managed only one goal this season and has often found himself left out of the team.
He started Sunday's defeat to Manchester City on the bench but barely made an impression when he did come on:
The Chilean was an inspirational force during his time with Arsenal. He was an energetic presence in attack, supplying goals and assists, but he looks an increasingly disconsolate figure at Old Trafford.
Former Gunners boss Arsene Wenger has explained why he thinks Sanchez is struggling at United:
The forward is keen to leave Manchester United after failing to settle in the north-west, according to Paul Hirst at The Times. He is seen as an "aloof figure" and rarely speaks to his team-mates, other than David De Gea, Juan Mata and Romelu Lukaku.
Sanchez's agent, Fernando Felicevich, has offered the Chile international to Real Madrid ahead of the January transfer window, according to El Chiringuito (h/t Sport). Los Blancos are keen to strengthen their attack but have not entered into negotiations yet.
The 29-year-old will seek a move away from the club in January if he continues to struggle for game time under Mourinho, per James Robson at the Manchester Evening News.
However, Sanchez's huge wages are likely to prove a stumbling block that could scupper any potential move, particularly with him performing poorly on the pitch and failing to justify the outlay which would be required to sign him.
PSG remain one of the few clubs who could afford him, but unless one of their famed attacking trio was to leave, there looks to be no room in the squad.
Neymar and Mbappe have both interested Real Madrid, journalist Guillem Balague has told Express Sport (h/t Jack Otway at the Daily Express). If either player were to leave the French side, it could open up a path for Sanchez to swap Manchester for Paris.