It is understood that Sunderland and Birmingham were also interested in the 29-year-old but Villa edged them out and are now on the brink of securing the deal.
The Championship side also reportedly have an option to buy the Scottish international at the end of the loan spell.
Snodgrass is already familiar with Villa boss Steve Bruce, after they worked together when Bruce was in charge of Hull.
The Hammers only signed Snodgrass from Hull for £7.5m last January but he was told by Slaven Bilic earlier in the window that he isn't in his plans.
If Villa sign Snodgrass, that could make way for Ross McCormack to join fellow Championship side Sunderland on loan from the Villains.