The 22-year-old forward is highly rated, has scored five goals and has as many assists to his name in Ligue 1 this season.
His performances have led to interest from a number of clubs in Europe and he has been heavily linked with a move to England.
Watford are believed to be interested in snapping up the forward, but it has been claimed that there is Premier League interest in Muani as well.
According to French outlet Foot Mercato, Southampton are interested in taking the forward to the Premier League in the summer as they look to bolster their squad.
The Saints have already taken the first steps in their attempt to sign him and are in contact with his entourage.
Southampton are convinced that he could be a good fit for their side and are preparing to secure a deal to sign Muani.
They are ready to offer a fee of around €5m to take the forward to St. Mary’s in the summer.
His current contract with Nantes will expire at the end of next season.