Laws has threatened to start looking elsewhere, but Tigers boss Taylor insists it is out of his hands.
He told the Hull Daily Mail: "Right now, it's dragging on a little bit and I imagine Brian is getting a little bit frustrated.
"They've offered £100,000 and I've accepted it so the rest is down to Kevin now.
"At this moment, Kevin is taking his time on the decision. I said to him that if he wants to go there he can, I wouldn't stand in his way."
If the transfer goes through, it will mean City get a full return on the £100,000 paid to Chester when Ellison moved to Hull in January 2005.
Liverpool-born Ellison has scored twice in 28 starts and 13 substitute appearances in his year and a half at Hull City.