The 18-year-old, who made 18 appearances in the French top flight last season, can play in both central defence and midfield and is being tracked by a host of clubs across Europe.
But reports in France say it is Villa who are currently in the best place to sign Canvot, having watched him at the recent Maurice-Revello tournament in which he starred for France’s under-20s.
Toulouse are thought to value the player at around £17million and with four years still to run on his contract, a deal would not be cheap.
Villa boss Unai Emery wants to strengthen his defence this summer, with the focus on recruiting a right-sided centre-back to provide back-up and competition for England international Ezri Konsa.
Axel Disasi, who spent the second half of last season on loan from Chelsea, has now returned to his parent club leaving Villa a player light in the heart of defence, with Emery ideally wanting two players to cover each position.
Villa also want a right-back and a winger with the future of Leon Bailey set to become clearer once he has returned from his summer break.
Bailey, who recently played for Jamaica at the Gold Cup, left the pitch in tears after the final home match at the end of last season and is the subject of serious interest from clubs in Saudi Arabia.
Villa, meanwhile, have confirmed 19-year-old defender Thierry Katsukunya has signed a new contract. The Wales under-21 international was a regular for Villa’s under-21s last season.