Burley announced his resignation at Derby manager on Tuesday and The Lions are close to announcing a replacement for Denis Wise.
"I came close to making an appointment recently, but now a new candidate in George Burley has emerged," Burnige has told the official Millwall website.
"Given what he has achieved in the game, I am bound to be interested in someone of his quality.
"I can confirm that the wheels are in motion, although I still want to keep my cards fairly close to my chest.
"I anticipate making a further announcement next Tuesday."