The 20-year-old continued to impress his Premier League admirers last year despite Donny's relegation from the Championship on the final day of the season.
Sky Sports News claims that Tigers manager Steve Bruce has been keeping an eye on the highly-rated Husband and believes that he has the potential to make the step up to the top flight.
Hull are believed to have contacted Rovers to start negotiations over his transfer, which Doncaster boss Paul Dickov admits that he is helpless to stop if Husband does not accept an improved deal at the Keepmoat Stadium.
Dickov told The Star:: "We need to sit down and have conversations with James and his advisers to find out whether he wants to stay.
"It's pointless us putting a new deal to him if he has his heart set on leaving. I won't stand in anyone's way if they express the desire to leave because what I can do now is offer players long-term security and buying into the long-term success of the club.
"If someone doesn't want to be part of that, in the nicest possible sense, they can go. If he wants to stay, no doubt there will be a new contract offer."
Husband has made 73 appearances for Doncaster, scoring four times, since debuting in 2012.