Peter Taylor revealed to the Hull Daily Mail: "I know there's another couple of clubs that want to talk to him as well so, of course, like any footballer people like to show respect and go to talk to the clubs.
"I'm sure that will happen but I'm hoping we do get the green light. If he does have to go to talk to other clubs I understand that. If not we'll get it sorted out the early part of the week."
He described the player as "a very, very rugged left back that I would not want to play against."
He added: "He used to be a bit aggressive. He seems to get his body in the way all the time. Unfortunately, he's had a career where he has had too many injuries, otherwise he could have gone on from there."
Edge started his career with hometown club Gillingham, where he played under Peter Taylor during his spell as manager there. The 5'9" defender made just over 100 league appearances and scored once before signing for Hibernian last summer. He started 20 SPL games and picked up a League Cup losers medal.
Cover for the left-back position has been much needed, being highlighted by injuries to Andy Dawson last season when Damien Delaney and Alton Thelwell had to be used as makeshift left-backs.