The Hammers were rebuffed in their two earlier approaches this month as they failed to meet the Tigers’ valuation.
However, after Burnley agreed a £10m offer today, Sky Sports claim West Ham have returned with the same amount.
Middlesbrough have also shown interest in Snodgrass, but their bid which does total £10m is structured differently, making it less appealing to Hull.
Hull's Robert Snodgrass is understood to prefer a move to West Ham over Burnley
West Ham rebel Dimitri Payet continues training with the reserves
Tue, January 24, 2017
West Ham want-away Dimitri Payet has been snapped training with the reserves again
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Dimitri Payet was snapped training with the West Ham reserves today
It will now be up to Snodgrass and his representatives to agree personal terms
According to The Guardian, the 29-year-old favours a move to West Ham or Middlesbrough, with Burnley unlikely to match his wage demands.
Slaven Bilic is looking to strengthen out wide, with Dimitri Payet still looking to secure an exit for Marseille.
And it will now be up to Snodgrass and his representatives to agree personal terms.
The ex-Leeds man refused to sign a new three-year contract last month at the KCOM Stadium, and an exit before deadline day now looks extremely likely.
Despite Snodgrass being key to Hull's chances of survival, the club are ready to sell with his contract up in the summer of 2018.
Meanwhile, West Ham are aiming to secure a striker before Tuesday's deadline, with Brentford's Scott Hogan still on their radar.