The Ivorian striker's future has been the subject of much speculation after a troubled start to the season was followed by reports of a meeting with representatives of Italian champions Internazionale.
But Kenyon remains adamant Drogba will stay and honour his contract, which runs until the end of next season.
Kenyon told BBC Sport: "Didier's under contract for the next 18 months. He will be going nowhere in January."
He added: "Whether people leave Chelsea is as much down to us as anybody else. I don't know whether he did or he didn't (meet Inter representatives).
"But he's a big player for us and we want him back. He's one of those players who can make a difference."
Drogba has been regularly linked with a move elsewhere with Inter, now led by former Chelsea boss Jose Mourinho, the current favourites to entice him away from Stamford Bridge.
Reports of a meeting with Inter sporting director Marco Branca and Mourinho's agent Jorge Mendes emerged in the build-up to the Blues' Champions League clash with Bordeaux.
Luiz Felipe Scolari denied he knew anything of the revelations and said: "I do not sleep with Drogba."
Drogba himself has done little to douse the flames of speculation, the striker merely reiterating he had a contract with Chelsea until 2010.
The former Marseille player has endured a difficult season and having missed the start of the campaign through injury he is yet to open his Premier League goals account.
And the 30-year-old is currently serving a three-match ban for throwing a coin back into the crowd during the Blues' Carling Cup defeat to Burnley.
But despite Drogba's problems, Kenyon appears determined to hang on to him, meaning there is little likelihood of Chelsea delving into the transfer market come January.
"I don't think we will be doing any business in the January transfer window because the type of players we are looking for are not available," said Kenyon.
"Another reason is that we have still got some long-term injuries coming back and in January or February, Chelsea will have more player availability.
"We put our squad together in the summer and we are concentrating on the squad we have and making sure our players get back from injury. On that basis, we think we have got a good enough squad to improve on last season."