In 2014, the Magpies spent £5m to sign Riviere from AS Monaco, but the Frenchman has contributed just three goals in 31 appearances in all competitions.
After returning from a loan spell at Osasuna, Riviere remains down the pecking order at St James' Park but it appears that the versatile attacker has emerged as a transfer target for teams in France and Turkey.
According to the Newcastle Chronicle, Metz and Osmanlipsor are prepared to offer him an escape route from the North-East and Newcastle are unlikely to stand in his way should they receive a solid offer.
Last season, Metz were one of the lowest scorers in Ligue 1 as they finished in 14th place in the standings, while Osmanlispor were similarly disappointing in the final third as they claimed 13th spot in Turkey's top flight.
The 27-year-old has one year remaining on his contract.