Grandsir has scored two goals, creating four more, and has shone against Paris Saint-Germain and other top-level opponents.
And French media claim Toon and Cherries officials have opened talks with their Troyes opposite numbers about the right winger, 21.
Normandy-born Grandsir joined Troyes from hometown club Evreux in 2012. Under contract until 2019, he has seen his value soar to £4 million this season.
Troyes are reluctant to part with their prize asset next month. But despite being based in Champagne country they have more of a brown ale budget - and they will be unable to resist a bid from the Premier League.