Slaven Bilic's battling to keep his job at West Ham United after today's defeat at St James's Park.
Newcastle United beat Bilic's side 3-0 this afternoon to get their season up and running.
Sky Sports claim that Bilic's position is now "under review" after a losing start to the Premier League campaign.
They report that West Ham remain "big admirers" of Benitez.
Fulham manager Slavisa Jokanovic has also been named as a potential successor.
Newcastle manager Rafa Benitez came within two hours of taking the West Ham two years ago. Benitez, 57, instead took over at Real Madrid after a last-minute approach from his boyhood club.
Benitez, however, still has a good relationship with West Ham co-owner David Sullivan, and it is highly likely that he would make the club's shortlist – if Bilic loses his job.
Benitez, tellingly, claimed yesterday that he no longer saw the Newcastle job as a "long-term" project.
"My aim is trying to improve things, so when I leave, whenever it is, I would like to be sure that the team and the football club will be better," said Benitez, who has repeatedly aired his frustrations at the club's efforts in the transfer market this summer.
Benitez, under contract for another two years, will not resign from his post – and Newcastle owner Mike Ashley will not sack him.
But the Spaniard could, conceivably, still leave Newcastle this season to take a position up at another Premier League club.
However, West Ham – or any other club – would have to pay a release clause of more than £5million to take him, and the London club have previously backed away from paying compensation for managers.