The 40-year-old has had just one year in management but steered Derby to the Championship play-offs in his sole campaign.
He is renown for his club-record of 211 goals in a stellar Chelsea career from 2001 to 2014, and racked up 106 caps for England.
Lampard has been strongly linked with the job since Maurizio Sarri left the role this month.
In a statement Derby said: "With pre-season fast approaching for both clubs it is hoped this will allow Chelsea to swiftly conclude their discussions.
"The club will make no further comment until it is appropriate to do so."
Lampard has two years left on his current Derby contract.