The Principality club are on the lookout for a new striker as star player Radamel Falcao has been ruled out for the season and they seem to have turned their attention towards the Italian forward.
Quagliarella has already rejected Norwich and Valencia, but he could be tempted by the proposal from France, especially with Juventus set to complete the signing of Pablo Osvaldo from Southampton.
The 31-year-old has seen little playing time this season, starting just 3 Serie A fixtures, while making another 11 substitute appearances.
Since joining the club from Napoli back in 2010, Quagliarella has managed 23 goals in 81 Serie A outings.
Meanwhile, Monaco are locked in the battle for the Ligue 1 trophy with Paris Saint-Germain and Claudio Ranieri’s side are 21/20 to see off Lorient at the weekend.