The striker moved to St James' Park from Monaco in the summer of 2014 for around £6m after impressing in France.
However, the 26-year-old has struggled to find his feet in England and he is now ready to leave Newcastle.
Osasuna, according to Diario de Navarra, will be Riviere's new club and he is close to finalising a loan move.
The Frenchman will join the Spanish side for the whole of the upcoming season - before potentially joining them permanently next summer.