Reports claim the Rams will pay £7million for his services as they look to bolster their squad after a poor start to the Championship campaign.
Gary Rowett's side have only picked up one point from their first two games and Lawrence's arrival could help their cause.
Derby have other targets on their wish-list but Lawrence's deal could be done in the coming weeks.
He has enjoyed a number of loan spells at Carlisle, Yeovil Town, Rotherham United, Blackburn Rovers, Cardiff and Ipswich Town but his future at Leicester does not look promising.
Lawrence has come off the bench on just three occasions to play in the Premier League for the Foxes, with Derby now looking ready to give him a fresh challenge in the Championship.