Hull boss Steve Bruce is keen on taking Snodgrass - who scored seven goals for the Canaries last season - to the KC Stadium in time for the 2014/15 season.
Talks are believed to have taken place between both sides, with the Tigers hopeful of snapping up Snodgrass by the start of next week.
Snodgrass - a childhood Celtic fan - was linked with a January move to the Hoops after Neil Lennon watched him during an FA Cup tie between Norwich and Fulham.
The 26-year-old has scored 12 goals for Norwich in 61 appearances since joining from Leeds United.
He scored the only goal in Scotland’s 1-0 World Cup qualifying win over Croatia in June 2013, consigning the Croatians to their first competitive home defeat since 2008.