The Lions' chairman expected to be able to make an announcement shortly but has warned fans not to believe what they have read in the national newspaper so far, with Lawrence emerging as the latest "big name" favourite.
Yeovil's Gary Johnson, Bees boss Martin Allen and Judas Iscariot-wannabe Teddy Sheringham have all been linked with the vacancy but Burnige has denied that any of them have been offered the job, although he did confirm he was interested in former Southampton boss Steve Wigley.
"I am down to two people who would deserve the job", said the Chairman. "and if I am quite lucky, there will be a decision next week.
"What I have warned fans about has turned out to be true - I have not seen anything in the national press that bore any resemblance to the truth.
"I want someone with the same passion for the club as the supporters."