The 26-year-old has two years remaining on his current contract at White Hart Lane.
Huddlestone made 29 first-team appearances for Spurs last season, but manager Andre Villas-Boas is understood to be willing to sell him.
The four-time England international has attracted interest from Fulham, Sunderland and Cardiff City in recent weeks.
However, according to the Daily Mail, Hull bosses are hopeful of winning the race for his signature.
Huddlestone has not scored a goal since April 2011 and, in a bid to raise money for Cancer Research, he has vowed to not cut his hair until he finds the net again.