Leeds target Abel Hernandez is one of four players offered new contracts by Hull after they issued their released list.
The Uruguay striker missed almost seven months of the season after rupturing his Achilles in the 3-2 home defeat to Wolves on August 15.
Hernandez still managed an impressive tally of eight goals in 10 appearances and he must now decide whether to take up the option of a new deal at the KCOM Stadium or move on.
Defender Max Clark, along with midfielders Seb Larsson and Moses Adubajo, have also been offered new deals by the club.
Goalkeeper Allan McGregor was given the opportunity to stay on Humberside but opted instead to return to former club Rangers.
Ex-Sunderland defender David Meyler is among the players released by the Sky Bet Championship side, while the Tigers remain in discussions with centre-back Michael Dawson over his future with Hull.