The France U21 international is the latest player lined up by Villa, who are also due to give medicals to strikers Emmanuel Adebayor and Rudy Gestede.
A third forward, Jordan Ayew, has already arrived this week along with full-back Jose Angel Crespo.
The new man in Tim Sherwood’s sights is a 22-year-old who has been a regular in the Nantes side for the past four seasons.
The French club’s president this week told newspaper L’Equipe he had sanctioned Veretout’s move to Villa despite a better offer from Leicester.
Waldemar Kita said: “I am not going to go against the boy. He is a boy who has never done us wrong, who played the game right until the end, contrary to others, who did not sulk.”