Terry has been on the coaching staff at Aston Villa since October, helping Dean Smith's team beat the Rams to clinch promotion in the play-off final at Wembley.
The Daily Mail says Derby have been impressed by the former England captain and could hand him his first shot at management if Lampard departs for Stamford Bridge.
Rams owner Mel Morris hired Lampard last season without him having any experience.
It proved to be a good decision as the 40-year-old guided the club to the Championship play-off final.
Derby and Chelsea are yet to hold official talks over a compensation package for Lampard.