Sky Sports News reports that Derby have made a £2m bid for the four-time England international, triggering a clause in his contract following Hull's relegation from the Premier League last season.
Huddlestone will now discuss personal terms with Derby, where he began his career as a 16-year-old and made almost 100 first-team appearances before joining Tottenham Hotspur in June 2005.
The 30-year-old made 23 Premier League starts for the Tigers last season but was unable to prevent them from suffering relegation to the Championship.
The likes of Newcastle United, West Bromwich Albion and Birmingham City have also been credited with an interest in Huddlestone, but Derby have now emerged as favourites for his signature.
Huddlestone has scored eight goals in 172 appearances since joining Hull from Spurs in 2013.