Current boss Sarri is expected to leave the club this summer to take over at Juventus, and if that happens, Lampard will be among the favourites to be named as his successor.
When asked about the prospect of Lampard taking charge, Drogba said: "Every summer is big. I think he is a very good option for the club.
"He’s done well with Derby, taking the team to the play-off final and I think it’s a very good option for the club."
Lampard has just one season of managerial experience under his belt, but 41-year-old Drogba rejected the idea that the Derby boss isn't ready to step up.
"He’s never going to be ready then? Does he have to wait until he’s 40 or 50 to be ready? No.
"I think it depends on experiences, it depends on your desire to succeed and do it if he feels ready. It’s not too early."
Drogba was speaking at Stamford Bridge during a training session for Soccer Aid 2019 which will be held at the west London ground.
He scored 164 goals in 341 games for the Blues across an eight-year stretch and a season-long comeback.
"I’m very happy to be here, back in the stadium where I’ve scored so many goals, celebrated so many titles," he said.
"It’s always good to be here, and Sunday is for a good reason, a good cause in Soccer Aid and I’m really glad to be part of this team and contribute.
"I will always follow [Chelsea]. I spent nine years here so I will always follow the results and how the club is going."
When asked whether Drogba himself harbours dreams of sitting in the managerial hot-seat at Stamford Bridge, a grin spread across his face, but he wouldn't comment on what the future holds.
Soccer Aid for Unicef will be broadcast live on ITV on Sunday 16th June, starting at 6.30pm.
To donate to Unicef, visit socceraid.org.uk
