The Daily Mail says Tottenham are interested in a summer move for the 23-year-old.
But they have competition in the form of Paris Saint-Germain, who have been impressed with the way he has taken his game to the next level under Steve Bruce.
The report claims that Spurs would be willing to include Danny Rose and Juan Foyth in the deal, with additional cash if required.
Rose is currently on loan at Newcastle until the end of the season and Spurs boss Jose Mourinho is keen to clear out his squad of any deadwood.
Bruce though, is insistent that Saint-Maximin is not for sale at any price.