The offers from West Ham and Burnley are in the region of £10m, though the Hammers' is higher.
Clarets boss Sean Dyche said there was a "difference" between a fee being agreed and "a player joining".
Meanwhile, Middlesbrough boss Aitor Karanka says his club are "working on offers with Hull".
"I think they rejected an offer but we are working, " he added.
Snodgrass has scored seven league goals this season for the 19th-placed Tigers.
West Ham's proposal comes a day after Burnley's bid and is their latest attempt to sign the player this month - they previously had offers of up to £6m rejected by Hull.
The Tigers say the move is now down to the player and he has not yet gone for a medical at Burnley.
"It's an ongoing situation. There's no imminent moment that the player is here or going to sign," added Dyche.
"In theory they gave us a chance to speak to the player and take it from there. I get the feeling there are a number of clubs who have been interested."
Snodgrass missed Sunday's 2-0 defeat at Chelsea with what manager Marco Silva described as "a small injury in the knee".
Silva is reluctant to part with Snodgrass, having already sold midfielder Jake Livermore to West Brom for an undisclosed fee, believed to be £10m.
Snodgrass has been linked with a move since December, before Hull triggered a one-year contract extension, tying him to the club until the end of the 2017-18 season.
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West Ham have joined Burnley in having an offer accepted by Hull for Robert Snodgrass, while Middlesbrough say they have also made a bid.