Moyes left the club on Tuesday (May 15) after coming to the end of the six-month contract the Scot signed in November and Benitez is top of a five-man shortlist drawn up to replace the 55-year-old.
What about Newcastle?
The report says that the new boss will be "backed with substantial funds", which is something that has irked the Spaniard during his time at St James' Park.
Benitez feels that Magpies owner Mike Ashley has not supported him in the transfer market after getting the club promoted to the Premier League as Championship winners in 2017 and the Evening Standard reports that the former Chelsea and Liverpool chief wants £80m this summer to rectify that.
Ashley promised to Benitez in a statement at the end of the season that; "every penny generated by the club is available to him" - but whether that will meet his demands remains to be seen.
Key players at Newcastle have spoken publicly about their support for the 56-year-old, with Ayoze Perez telling the Chronicle:
"We have to look after him, take him seriously and listen to what he wants, and hopefully we can keep him here."
With the fans already very much in Benitez's corner over Ashley's, if he were to leave for the Hammers because of a lack of funds it could prove to be a decision that the owner could not recover from in their eyes, which gives the manager far more power during his current contract negotiations with managing director Lee Charnley.