Drogba, 33, is in the final year of his contract and has been linked with a move away from Stamford Bridge, with clubs in China believed to be ready to offer him a lucrative move to Asia.
The striker bagged his 150th goal for the club on New Year's Eve and bowed to the crowd, which was interpreted by sections of the media as a goodbye.
Drogba is currently with Ivory Coast preparing for the African Nations Cup and it has been suggested he may have played his final game for the club. But Villas-Boas is hopeful of keeping the veteran forward at Stamford Bridge.
"Not that I know of," Villas-Boas said in response to a question about whether a bid had been made for Didier Drogba and his fellow forward Salomon Kalou. "When they return, they will return to this club and hopefully we will hold on to them until the end of the season."
Villas-Boas boss confirmed Josh McEachran would go out on loan for the rest of the season - in all probability to Swansea - after Saturday's game with Sunderland, and also said Gael Kakuta's loan move to Dijon had not been concluded yet but he expected it to happen "soon''.
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