An offer for the 25-year-old was turned down last week, but after an increased bid it looks like the League Two club are set to allow Ellison to talk to the Tigers.
Chester chairman Stephen Vaughan revealed to the Chester Daily Post: "The revised bid from Hull has been received. The financial offer has been increased to a six figure sum, and the two players that have been offered are a striker and a defender. Unfortunately, at the moment, I am not at liberty to reveal their names."
The striker in question could be any one of Danny Allsopp, Aaron Wilbraham, Clayton Donaldson or Birkenhead-born Jon Walters, who have all struggled to establish themselves this season. The defender is probably Richard Hinds, Alton Thelwell or Nathan Peat, who are all out of contract at the end of the season anyway and unlikely to be offered new ones after making only a handful of first team appearances for City between them this season. There is also the possibility that the two players in question will only be going on loan rather than a permanent move.
Vaughan continued: "Basically, if Kevin Ellison says he wants to move to a club at a higher level, then we couldn't stand in his way. However, if he wishes to stay with us, then that is fine.
"It's always flattering when other clubs show interest in our players, but as I always say at these times, we are building a quality squad here at Chester not dismantling it."
Elsewhere, Peter Taylor hopes to extend Stev Angus's loan spell at City.