According to Foot 365, as cited by Get French Football News, the 31-year-old French midfielder and free agent rejected a Premier League return because he was holding out for a move to Lyon, who he hoped would turn to him to replace the reportedly outgoing Nabil Fekir.
While both Liverpool and Chelsea expressed interest in Fekir, no deals were completed and the French international looks set to remain at his current club - meaning Ben Arfa's move would not be happening.
The player is a free agent after his contract with French champions Paris Saint-Germain expired this summer.
He had earned the move to PSG after impressing in Ligue 1 for Nice.
Ben Arfa made a total of 86 appearances in all competitions for Newcastle, scoring 14 goals - including a memorable strike against Bolton Wanderers - and becoming a fan favourite.
However, in the latter stages of his time on Tyneside he fell out of favour with manager Alan Pardew, famously being banished to train with the reserves following a dispute.
The Frenchman was then sent out on loan to Hull City for the 2014/15 season but made just eight Premier League appearances.
His time with Hull was plagued with problems too. In December 2014, Ben Arfa unexpectedly left England, with then Hull manager Steve Bruce later admitting he did not know where the player was and that his career with Hull appeared to be over. He was released from his Newcastle contract in January 2015.
He was similarly forced to play with the reserves at PSG too, prior to being released by the club this summer.
It remains to be seen whether West Ham will attempt to go back in for free transfer Ben Arfa, now it's clear a move to Lyon isn't going to happen. They could still sign the player despite the transfer window being shut since the Frenchman does not currently have a club.