The 23-year-old has started just four Premier League games under manager Maurizio Sarri, which has led to speculation surrounding his future.
The Denmark international has been linked with moves to Barcelona and AC Milan in recent months.
But Christensen sees his future at Stamford Bridge – and the news will come as a boost to the Blues, who are facing a two-window transfer ban.
He said: “It is always difficult when I speak in Danish and it gets mistranslated. I haven’t had a conversation with the club but I want to stay here.
“I’ve said I’d like to stay, but they haven’t said I’m definitely staying. I’ve said what I want to happen and that was definitely staying.
“I’ve still got a long contract (until 2022). I’m still proud to be a Chelsea player. I’ve been here since I was 16. The club have done a lot for me.”
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Despite his lack of league action, Christensen has featured regularly in domestic cup and Europa League games this season.
He added: “For me personally, the cup games and the Europa League this season have been very important, it has kept me up to speed.
“Obviously I want to play every game but it has taken the frustration a little bit out of it, getting playing time, and it has helped me a lot.