The Sun says Lampard wants the Ivorian to join his backroom staff as a striker coach.
Drogba was part of the same successful Chelsea side which won numerous Premier League titles and were crowned Champions League winners during a golden period from 2004-2012.
He reportedly sat down for lunch with Lampard this week, after talking up his former teammates credentials for the role.
Drogba said previously: "Frank has done well with Derby, you know, taking the team to the play-off final.
“I think it is a very good option for the club [Chelsea]."