The Hammers have dropped into the relegation zone following their 2-0 defeat at Tottenham Hotspur on Sunday.
The pressure has been mounting on Moyes who has struggled to replicate the performances of the last two seasons where West Ham qualified for Europe.
There are question marks over how long the Scot could continue as West Ham manager given the kind of money he spent last summer.
But it has been claimed that the West Ham board have no intention of sacking Moyes at the moment.
Many believe that the home game against Nottingham Forest could be make-or-break for the Scot in terms of his future at West Ham.
However, the club do not have the appetite to sack a manager who got them back to playing European football.
It has been claimed that the West Ham board are encouraged by the performances West Ham put up against Newcastle and Chelsea.
The Hammers have a tough run of fixtures coming up after Forest where they will take on Manchester United in the FA Cup and then Brighton, Aston Villa and Manchester City.
