The Canadian forward, 21, originally had an offer placed on the table in July and is believed to be prepared to stay.
However "little technicalities" have stood in the way of an official agreement, though Kean does not expect any further snags.
"I think it will be done in the next couple of days," he said in the Lancashire Telegraph on Saturday.
"It's dragging on a bit now and there are only a couple of little technicalities in it, the broad base of it's agreed.
"That took quite a while to get there but the boy seems happy and we just want to get it put to bed and get him focused now. "
Kean is wary of the psychological effects contract negotiations can have on players and indeed support, further adding to his desire to end the saga.
"It would be good for the supporters," Kean added. "He showed certainly at the end of last season what he can do and I'm anxious that he can put his contract thing behind him, get him signed and get back to that form.
"Because no doubt if you keep on talking about new contracts it's spinning about somewhere in your head, and we want to get that nailed and put to bed."