Gibb has drawn up a shortlist of three possible candidates, which include, according to reports, former Middlesbrough manager Bryan Robson and ex-Leeds player and Sky reporter Chris Kamara.
Although Bradford are second from bottom in Division One, Gibb states they have a brighter future on and off the pitch than Leeds.
He told the Bradford Telegraph & Argus: "I think there are more positive angles to our job that at Leeds at the moment.
"I think there are more positive propositions from a challenge point of view."
Meanwhile, Kamara pulled out of the running today when he said he no longer wished to be considered for the post.