The four players, who arrived from Ligue 1 in the summer, were among the 13 players that landed at Villa in a £55million transfer spree last summer.
Amavi was improvise prior to his season-ending injury, while Ayew, Veretout and Gana have been decent at Villa Park but the club wants to recoup their money as they plan for life in Championship next season.
It is believed that Marseille are showing interest in Gana while AC Milan are watching Veretout closely. Amavi and Ayew are expected to attract interest and are unlikely to make the move down to the second tier.
Villa are rooted to the bottom of the Premier League table, nine points of the safety, and are overwhelming favourites for the drop.
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