Drogba, 34, snubbed Chelsea's offer of a one-year contract extension, while they in turn refused to bow to his demands for a two-year deal.
Lampard said: "I'm desperate for him to stay. He is a magnificent player. He's a machine.
"His body is a machine, when you look at him stripped down. He's lost no pace, he's lost none of his finishing instinct.
"As a man, I love Didier and whatever he decides to do, whether he stays or whatever, he has been a hero for this club and will go down as a legend."