Drog, 34, is a free agent at the end of the season.
But skipper Terry insists the striker who set a new FA Cup final scoring record must stay.
JT said: "It will be such a shame if Didier leaves because he has been incredible for this club.
"Didi loves Chelsea and I really hope he will be back next season.
"We've got a massive Champions League game in a couple of weeks and after that hopefully something can be thrashed out and he stays."