The Ivorian is in the final year of his contract and has been linked with a transfer to China to link-up with former strike partner at the Blues, Nicolas Anelka, at Shanghai Shenhua.
However, after a strong end to the season under Roberto Di Matteo, the duo hopeful Drogba will decide to stay at the club but feels even if the striker leaves he will have left a lasting legacy at Chelsea.
Lampard told reporters: "I am desperate for Didier to stay. He is a magnificent player. He has lost no pace, none of his finishing instinct, but as a man I love Didier and whatever he decides to do, stays here or whatever, he has been a hero for this club and he will go down in memory as a legend.
"The amount of important goals he has got for us in Cup finals and important games throughout his career makes him an icon, a historical figure at Chelsea, without a doubt."
Skipper Terry added: "It will be such a shame if Didier leaves because he has been incredible for this club. Didier loves Chelsea and I really hope he will be back next season."
Chelsea have prioritised bringing in a striker over the summer to boost their Premier League title chances next year after a disappointing league campaign, with names such as Gonzalo Higuain, Hulk and Radamel Falcao rumoured to be on their shortlist.
Lampard feels whoever replaces Drogba in the future will have a tough job following the success the Ivorian has had in his eight years at the club.
Asked if Drogba would be a hard act to follow, Lampard said: "Of course it would be because there is no one like Didier as a player, not with the bulldozer thing he's got, with the sublime finish and touch he has got.
"Clubs always move on and eventually all of us will move on at some stage and you have to find a different way of playing. But for what he's done at this club he deserves everything. He's unique. He is not just that big man, he scores when it matters and that's just priceless."