Moyes has struggled to inspire a revival at West Ham in recent weeks and the Hammers are in the thick of a battle to survive in the Premier League.
The former Manchester United manager has come in for criticism and it had been suggested in some quarters that the Hammers are set to pull the trigger.
Ex-Liverpool and Real Madrid boss Benitez has been mooted as the man to come in and replace Moyes.
That talk though is wide of the mark and West Ham are not about to sack Moyes as manager.
They appear to be continuing to trust Moyes to lead the side out of trouble, despite just 15 points from 19 league games picked up on his watch this season.
Benitez was most recently in charge of Everton, but failed to win over the fans and was cut no slack despite a summer transfer window where he could spend just £1.7m.
The Spaniard remains a free agent, but it does not appear he is poised to become the new West Ham boss.
