BBC Radio Humberside understands that there are four Premier League teams interested in the 29-year-old midfielder.
The Scotland international has scored seven Premier League goals this season.
He was linked with a move away from the club in December before the club triggered a one-year contract extension, tying him to them until the end of the 2017-18 season.
Hull City have rejected a bid from West Ham for top scorer Robert Snodgrass.