The winger, 29, was eyed by the Ligue 1 champions last year, but he decided to join the Red Devils from Arsenal instead.
He has struggled since his Old Trafford arrival though, and has been dropped by United boss Jose Mourinho on a number of occasions.
The Chilean ace earns a staggering £505,000-a-week, and is by far the highest paid earner in the Manchester United squad.
And PSG would be willing to take Sanchez off their hands as long as they can land him on the cheap or even on a possible free transfer.
It is understood the idea of getting him off there books has been talked about by the United hierarchy.
The French giants are expected to lose one of Neymar or Kylian Mbappe next summer, and would need a superstar replacement.
An Old Trafford source said: “There has been some whispers that PSG want to take Alexis off of the club next summer.
“It's no secret he has struggled and not lived up to the expectations. He isn't getting any younger and it might never work for him.
“There was interest before the club signed him but he preferred staying in England at the time. That may have changed now.
“One of their top stars could go and it's not beyond the realms of possibility that a deal could be struck between the two clubs.”
Sanchez has been out-of-sorts at Manchester United, scoring just three times in 19 Premier League appearances.
He joined them from the Gunners last summer as part of a deal which took Henrikh Mkhitaryan to the Emirates.
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