The French side have made contact over a loan move with an option to buy, but it is understood Wolves are not currently willing to let him go.
The 22-year-old fell out of favour with Julen Lopetegui last season and was expected to depart this summer, but the club are currently eager to hang on to him as they assess their options.
Left-back Ait-Nouri has been playing on the left-wing in training games so far in pre-season and was previously used there by Lopetegui briefly last season.
Nice are still interested in striking a deal and will keep pushing, but reports suggesting talks are advanced are believed to be wide of the mark.
Other French clubs are also monitoring Ait-Nouri, who could yet depart later in the summer, despite Wolves’ current stance on him.