Lawrence is said to live close to Millwall's training ground and could fill the seat left by Dennis Wise.
It's said that Millwall Chairman Jeff Burnidge is looking for a more experienced manager.
Wise himself is attracting interest from new Championship side Southampton. Saints boss Harry Redknapp said
"I'd love to bring Dennis Wise here and I'm certainly trying to get him, but whether we can do it is another matter.
"I'm doing my best, we've made him an offer, but it may be that he feels he's better off elsewhere, that's the problem.
"But he's the sort of player I'm after, I want to bring in players with character and experience because it's going to be a very open division and a battle to go straight back up."