The left-sided midfielder - Chester's top scorer this season with 11 goals - is the subject of a £100,000 bid, which will also see two Tigers players go the other way.
Radio Merseyside report that Birkenhead-born striker Jon Walters and former Tranmere defender Richard Hinds are the players set to join the League Two side, probably on loan.
Peter Taylor says he is hopeful of having Ellison in his squad for the home game against Peterborough on Saturday when City again have to cope without 23-goal top scorer Stuart Elliott.