The 24-year-old joined Hull in 2011 from Leicester City and made 22 appearances in the Championship last season after missing the opening months of the campaign through injury.
However, despite being a regular en route to the Tigers' promotion to the Premier League, he could now be allowed to leave the KC Stadium.
It is understood that Forest are keen to sign the centre-half on loan, with manager Billy Davies looking to improve his squad.
Davies has seen two offers for Leicester defender Wes Morgan rejected and is happy to remain patient in his pursuit of new signings.
"We're making extremely good offers and we're certainly not chasing unrealistic targets," Davies told the club's official website.
"We know that there will be other negotiations for other players that will take a bit of time but there is a great effort here to conclude deals very quickly.
"All we can do is continue to ask the question and continue to put what we feel are very good offers into these clubs. Anybody that suggests that these targets are not possible are looking in the wrong direction.
"We'll keep doing what we can to convince other clubs that we mean to do some sensible business and we'll keep trying to bring players to this football club."