Villa had been low down the list of likely contenders, but were cut to 6/1 on Wednesday and are now as short as 3/1.
The Villans were already being tipped to add to their winger options before the close of the transfer window before Jack Grealish suffered a kidney injury at the weekend.
Aston Villa's Jack Grealish
And Ross McCormack's reportedly imminent loan move to Sunderland could free up funds for Steve Bruce to add to his Villa squad.
Bruce signed Snodgrass for Hull City three years ago, and the winger's form there was enough to tempt West Ham into a £10 million move for the 29-year-old in January.
Snodgrass has struggled to reach past heights at the London Stadium, however, and he was said to be in line for a swift exit, with Newcastle United, Brighton & Hove Albion, Leeds United, Norwich City among the clubs keen (Football London).
Wednesday were also credited with interest in the Scot and were odds-on favourites to sign him at one stage, but have since drifted to 5/1, behind Aston Villa and clear of Middlesbrough (14/1).
West Ham's Robert Snodgrass
The Owls are close to breaching the Football League's financial fair play regulations, head coach Carlos Carvalhal suggested this week, and are thought to have other priorities this summer.
Is West Ham's Robert Snodgrass bound for Aston Villa?