The Rams have been searching for a new manager since the departure of Gary Rowett to English Championship rivals Stoke last week.
Sky Sports reports a number of contractual issues still need to be addressed, but Lampard and Derby are keen to get the deal done.
Jody Morris, who has led Chelsea’s U18s to the FA Youth Cup in successive seasons, is expected to join Lampard as part of his coaching staff at Pride Park.
Lampard confirmed on Saturday that he was in talks with Derby over becoming the club’s new boss, with the 39-year-old keen to take his first steps into management.
The former Chelsea, West Ham and England midfielder was also interviewed twice for the vacant managerial position at Ipswich.
Lampard – capped 106 times by England – enjoyed a trophy-laden playing career winning three Premier League titles, four FA Cups, two League Cups, the Europa League and the Champions League.
Derby ended the 2017/18 campaign in sixth place, but failed to gain promotion via the play-offs, losing to Fulham in the semi-finals.