The 21-year-old is currently in his third campaign at Molineux after initially joining on loan from Angers in October 2020.
Since then, Ait-Nouri has contributed three goals and eight assists from his 64 outings, which have come from left-back or left wing-back.
When Wolves agreed a permanent deal with Angers last July, they negotiated a £9.8m with the agreement that the French club would receive a significant chunk of any fee should the player move elsewhere.
That effectively leaves Wolves in a position where they will have to raise well in excess of what they paid for Ait-Nouri if they are to make a profit.
However, before the World Cup break, the France Under-21 international lost his place to Hugo Bueno, who has since impressed on the left-hand side of the defence.
Although Ait-Nouri netted for Wolves versus Gillingham in the EFL Cup on Tuesday, it came from a late cameo outing as a substitute, and it appears that there is growing expectation that all parties may look to part ways.
According to Foot Mercato, Nice are ready to put forward a proposal to sign Ait-Nouri during the January transfer window.
While a potential transfer fee has not been suggested, it is reported that Nice have the finances to secure a deal for the player.
Nice are allegedly prepared to cut short the loan period of Fulham's Joe Bryan in order to accommodate the arrival of Ait-Nouri at the turn of the year.
With Ait-Nouri possessing a contract until 2026, and Wolves having a 12-month option to extend that, much may depend on the fee that Nice are prepared to pay for his signature.
At a time when Ait-Nouri is said to be open to an exit from Wolves, new head coach Julen Lopetegui is said to be considering his own choices at left-back.
Wolves have recently been linked with Sevilla and Argentina's Marcos Acuna, who Lopetegui worked with during his stint with the latter.