Snodgrass is out of contract in the summer but Hull do have the option of a further 12 months.
The midfielder has starred for the struggling Tigers with seven goals this season and the club have made a move to tie him down to a longer deal, but Snodgrass has reportedly rejected their offer due to off-field uncertainty.
The Daily Record now say Celtic will test the Tigers' resolve in January and hope a £4million fee will be enough to land the 29-year-old, although that figure could increase if Hull take up the 12-month option.
If Celtic do move for Snodgrass in the New Year they are likely to face plenty of competition for the Scotland international.
Celtic last week