Lawrence is currently out of work having departed Cardiff City in the summer.
Former Dundee United manager Ian McCall has also confirmed his interest in the vacant managers post at Ashton Gate.
Ironically the former Morton, Clydebank, Airdrie and Falkirk manager played with ex-City boss Tinnion during their time together at Bradford City.
He said: "This is the first job that interests me since I left United. I've been linked with lots of jobs but not applied for one."