Hamburg, Olympiakos and Stade Rennes are all interested in the striker.
It has been a busy summer for Newcastle, with eight new signings arriving at the club so far as manager Rafa Benitez has built a squad ready for the Championship.
There has also been a series of the departures with the Spaniard keen to clear out the deadwood in his squad and losing first-teams stars such as Georginio Wijnaldum and Andros Townsend.
Riviere is one of those who have allegedly been told they can leave, although so far he has failed to find himself a new club.
It appears that a move could be on the cards however, with the Chronicle reporting that three clubs are interesting in his services.
According to them, Hamburg, Olympiakos and Stade Rennes are all weighing up a potential offer, with the first two having already made enquiries.
The report fails to name what sort of price the Magpies are looking for, but it is likely to be far below the £6 million that they paid to bring him to the club.
There is every chance they will take the opportunity to send him out on loan with a permanent exit price included, as they have already done with Florian Thauvin this summer.