The Blues are now without a boss after Maurizio Sarri returned to Italy to join Serie A champions Juventus last week, and their former midfielder is the man expected to take over.
Drogba replied: "The one who is in talks now to get the job - Frank Lampard".
And the second-tier club are prepared to offer Lampard a lucrative new deal to try and keep him at Pride Park.
ESPN say Lampard will sign a three-year contract and be accompanied by former academy coach Jody Morris and long-time fitness coach Chris Jones.
The newspaper reports that Derby county "have launched a last-ditch attempt" to keep Lampard, who led them to last season's Championship play-off final.
Steve Holland, Nuno Espirito Santo, Javi Gracia and Erik ten Hag were also on Chelsea's wish list but it now looks like Lampard will return to the club he spent 13 years with as a player. "Yes, if it was him to take over the job, I believe in myself".
"You've got to have a manager that, first and foremost, wants to look", he told Sky Sports. Someone you have grown up watching, been at Chelsea forever.
"It's not my place to go over there and start talking to managers, but some managers aren't interested - they don't care about youth".
Asked about the prospect of Lampard taking over the job and developing the younger players who have been successful on loan, Abraham said that would suit his own career. "I think he will get it", he said. There is no better guy [than Lampard] to play under.
"Is he talking? I think he's talking and I think he's gonna get it".
"If you're going to make the approach, just make the approach; be open and transparent about it".
