The Ivorian's current deal is set to expire next summer and he is yet to commit his future to the club past that point.
The Blues insist there is no rush to tie the powerful striker down, with discussions regarding fresh terms ongoing.
Villas-Boas believes Drogba will sign when he is ready, with it difficult to imagine him breaking his emotional ties with the club after seven years at Stamford Bridge.
"I don't see it as a big issue," said the Blues boss.
"Players who are attached emotionally to this club - and Didier is attached emotionally to this club - will eventually renew their contract.
"So I go into no panic on that situation."
Chelsea are also hoping that Jose Bosingwa will extend his association with the club.
They activated a clause in his contract last year that kept him on their books for a further 12 months, but will see that agreement come to an end in 2012.
Talks have been opened with the 29-year-old full-back, with chief executive Ron Gourlay involved in the discussions, and Villas-Boas hopes his fellow Portuguese will pen a new deal.
"When you address renewals, it's always a good time to motivate people," he said.
"It's a situation where we are on top and judging according to what we feel best.
"We are in talks at the moment about the situation with the CEO and eventually with the players which we feel are right."