The 56-year-old Scot is the hot favourite to take charge of the Hammers for a second time, after Manuel Pellegrini was sacked on Saturday night.
West Ham co-owners David Sullivan and David Gold want an experienced figure to steady the ship with the club in serious danger of relegation – and they have earmarked Moyes as the ideal man.
In his previous spell at West Ham, the Scot steered the club to Premier League safety in 2017/18 having taken charge on a short-term contract in November 2017.
But, despite leading the Londonders away from relegation danger and to a 13th-place finish, Moyes left the London Stadium and Pellegrini was appointed in his place.
However, Sullivan and Gold are now ready to turn back to the 56-year-old, and are understood to have already opened talks over a deal.
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As in his first spell in the Hammers hotseat, Moyes will look to bring in Stuart Pearce as his assistant if he does land the job.
West Ham finished tenth under Pellegrini last season but this term has been a disaster, with ten defeats in 19 league games leaving them at serious risk of relegation.
Pellegrini’s expensively assembled side had actually started the season in fine form, but a run of two wins from 14 matches – and four straight home defeats – has seen them tumble from 4th to 17th in the space of three months.
Saturday’s 2-1 defeat to Leicester at home proved to be the final straw for Sullivan and Gold.