Arsenal star Sanchez could be on the move this month with Liverpool, Manchester City and Real Madrid all potential destinations.
The Chile international’s contract expires at the end of the season and a renewal is unlikely to be signed.
City appear to still be frontrunners for the former Barcelona star, with Pep Guardiola desperate to be reunited with the 28-year-old at the Etihad Stadium.
But Catalan newspaper Sport say there is a chance he may sign for Liverpool instead.
The Reds may have to land a top attacker if, as expected, Philippe Coutinho joins Barcelona.
Express Sport understands the Catalan giants are closing in on a huge £135million deal that will see him become the second most-expensive player in history.
Sanchez would fit the bill, particularly given what a hammer blow it would represent to Arsenal.
And Sport say that, though City remain keen to sign him, they may actually end up missing out because of what happened in the summer.
Sanchez seemed set to move to the Etihad after Arsenal and City agreed a £60million fee.
And when the deal fell through, City promised the player they would renew their interest in January.
But Guardiola has reportedly had a change of heart.
And with Sanchez determined to call time on his Arsenal career, Liverpool could benefit.
Meanwhile, Reds legend John Aldridge thinks the Gunners forward would be the ideal Coutinho replacement.
“Liverpool made a real statement of intent when they paid £75m to sign Virgil van Dijk,” Aldridge told the Irish Independent.
“And now they should put in a sneaky £40m offer to try and get Alexis Sanchez out of Arsenal.
“After a valuable 2-1 win at Burnley yesterday came with a dramatic late goal from Ragnar Klavan, there is a real feel good factor around Liverpool at the moment.
“And Klopp and the club have to make sure they keep that momentum flowing.
“The absence of Philippe Coutinho from the Liverpool team yesterday fuelled rumours that he may be on his way to Barcelona sooner than we expected.
“But that would not be so much of a concern if they could nick a player like Sanchez.”