A report claims the Villans will consider bids of around £10.8 million for the French left-back.
Amavi: A wanted man
Italian giants AC Milan and two Ligue 1 sides, one of whom is named as Lyon, are also claimed to have expressed an interest in the Frenchman.
The Reds have struggled in Amavi's position this season with Alberto Moreno widely criticised, and interest in Lorient's Raphael Guerreiro was recently reported.
Guerreiro (L) was a reported Reds target
However, with the Portuguese seemingly Borussia Dortmund bound, Liverpool could be forced to consider alternative targets.
Amavi was one of the few positives in Villa's season
Relegated Villa will reportedly consider bids of around €14 million (£10.8 million) for the 22-year-old they signed from Nice a year ago, as worrying rumours surrounding the club's proposed takeover continue.
Amavi, who has seven under-21 caps, was tipped to break into Didier Deschamps' France squad prior to his injury.
Liverpool have also been linked with a move for Leicester City left-back Ben Chilwell and have another, Australia international Brad Smith, already on their books.
Smith (R) is one of two left-backs on Liverpool's books