The Scotland international is due to fall out of contract at the end of the season and looks to be heading for the exit door next month after he rejected the offer to sign a new one.
Celtic have been heavily linked with a move for the 29-year-old, but the Magpies have now emerged as an interested party and are ready to bid £5million when the transfer window opens.
Reports claim that Snodgrass would be happy to drop down to the Championship as there is a very good chance he will be back in the Premier League next season as Rafa Benitez's men currently top the table.
Hull will do all they can to keep hold of Snodgrass and may prefer to lose him for nothing at the end of the season as they fight to stay in the top flight.
An offer of £10million would be hard to turn down, but it is claimed Newcastle are only willing to pay half that, and are confident it will still be enough.