The 28-year-old joined the Hammers in 2016 from Swansea for a club record fee of €24 million but due to injuries he has been unable to replicate the form that prompted the London-based club to break the bank for his services.
He has made 18 league appearances this season including nine starts, scoring three goals.
Swansea boss Carlos Carvalhal wants him back at Liberty Stadium to join their fight to beat the drop.
The Swans currently sit bottom on the log with 20 points, three points below safety.
"I never said we want anyone to go. If someone comes up we will look at it but as far as I am concerned, no-one is going," Moyes was quoted as saying by Tribal Football.
"I think there has been an offer [for Andre Ayew] but we wouldn't accept the current bid as it is," he added.
Andre Ayew could reunite with younger brother Jordan at Swansea if a deal is eventually struck.