Just two wins from their opening 10 games has put Slaven Bilic's job in doubt with supporters turning on the board and manager.
A host of managers have been linked with the Hammers job from Roberto Martinez to Carlo Ancelotti.
But Magpies boss Benitez is said to be top of the list, as reported by the likes of the Daily Star - and reports claim he feels he owes the club after turning them down at the 11th hour to manage Real Madrid when Sam Allardyce left the club.
West Ham threw away a 2-0 lead to draw 2-2 with Crystal Palace last time out much to the anger of supporters.
The performance showed the Hammers have class in their ranks but a lack of professionalism, focus and fitness.
Meanwhile Newcastle were the opposite as they showed plenty of discipline and the trademark Benitez organisation but a distinct lack of quality in their turgid 1-0 defeat to Burnley on Monday night.
Sky Sports pundits Jamie Carragher and Gary Neville both highlighted the fact Newcastle have a 'quality problem' which Carragher - a former player under Benitez at Liverpool - said would frustrate the Spaniard.
Benitez looked exasperated after the defeat despite his side sitting comfortably in midtable so should West Ham pounce now for the perfect marriage?
Bilic's time looks all but up and West Ham are desperately in need of some professionalism and a manager to get them organised.
And West Ham boast infinitely better attacking options than Newcastle with the likes of Javier Hernandez, Marko Arnautovic, Andre Ayew, Manuel Lanzini, Michail Antonio, Andy Carroll and Diafra Sakho in their ranks.
Their biggest failing is combining together as a team to get the best out of those players and Benitez is just the man for the job.