Leeds turned down a reported £1.5 million bid for Snodgrass three days ago with manager Neil Warnock keen to keep hold of the 24-year-old Scotland international.
But the Canaries, who already have former Leeds pair Bradley Johnson and Jonny Howson on their books, have returned with an offer "way in excess of £2million" and Leeds are currently considering whether to cash in on a player who has less than a year remaining on his contract.
Warnock made Snodgrass his captain shortly after taking the job at Elland Road in February and offered to make him the club's highest wage earner, but the Scot has so far opted not to commit himself to the West Yorkshire club.
Leeds confirmed on Monday that they had rejected Norwich's earlier approach for the player and Warnock said at the time: "It's difficult when players get their heads turned, but I'd like to keep Rob at the club and that's what I'm trying to do at the moment. Unless they come up with a valuation that the club thinks is satisfactory then that's what we want to do."
Leeds are currently in advanced takeover talks with potential new investors and confirmed earlier this month that they had granted due diligence to an unnamed group reported to be fronted by Bahrain-based Shaikh Abdulrahman bin Mubarak Al Khalif.