Clubs outside of the Premier League have until the end of the month to snap up players on loan, and Snodgrass has again emerged as a top target for Steve Bruce's Villa.
The Scotland international impressed while on loan at Villa Park last season as Bruce's men missed out on an immediate return to the Premier League, and they are keen to get him back.
The player himself would no doubt be interested in a return to the Midlands club, but the Hammers are not so sure.
Despite drafting in a host of new players throughout the summer, it is thought that Manuel Pellegrini wants to keep hold of Snodgrass, and will offer him the chance to fight for his place.
West Ham could review the situation in the winter transfer window, but for now it looks as though Snodgrass could be set to stay at the London Stadium.