The 25-year-old Russian international has long been linked with a move to England, with Manchester United having been previously credited with an interest in bringing him to the Premier League.
Blues boss Andre Villas-Boas has already signed one goalkeeper since arriving at Stamford Bridge last summer - Thibaut Courtois, 19, joined Chelsea from Racing Genk in his native Belgium before being immediately loaned out to Atletico Madrid for the 2011-12 campaign.
But, with question marks hanging over the long-term future of Petr Cech, and Courtois expected to spend another season out on loan, Villas-Boas is looking to bring in another new keeper.
However, Chelsea will now have to consider alternative options after Akinfeev revealed he has no intention of leaving CSKA.
Speaking to Russian newspaper Sport Express, he explained: "What has been published is not true.
"I recently renewed my contract with CSKA to stay here. I feel good at this club and I'm not negotiating with any others."
Chelsea have come into criticism for some poor defensive displays this season - the most recent of which a 3-1 defeat at Napoli in the Champions League on Wednesday.
With Villas-Boas under increasing pressure, it is a problem he will have to address, providing he is given the time to do so.