This would soften the blow for Aston Villa, as they have already lost midfielder Fabian Delph to Manchester City.
They are also expected to lose star striker Christian Benteke to Liverpool, as the Reds have met his £32.5m release clause.
Amavi has spent the last two seasons of his career with Ligue 1 club Nice, and he also spent the latter part of his youth career with them.
The 21-year-old defender has not officially agreed to a deal with Aston Villa yet, as he still has yet to agree to the final details of his contract.
However, Aston Villa appear likely to bring in the French international, who showed star potential with Nice in the 2014-15 season.
He scored four goals in 36 Ligue 1 appearances, showing that he may be able to emerge as a dual threat in the Premier League.
However, adjusting to the Premier League will be far from easy for the 21-year-old French star.
Liverpool CLOSE to completing £32.5m Christian Benteke deal with striker to miss Aston Villa friendly
DEFIANT Aston Villa boss says £32.5m SUPERSTAR will NOT go to Liverpool or Man United