The Scottish champions have made it clear to the Premier League table toppers that their star man, whom they are believed to value at £40 million, is not for sale.
The 20-year-old, who the Blues have been monitoring since he was at Fulham, has scored 20 goals in 38 games for Celtic following his arrival in the summer as Brendan Rodgers' side continue to dominate the Scottish top flight.
Dembele joined Celtic from the Cottagers for a mere £500,000 development fee last year and has risen in stature to become one of the most young forwards in world football.
Chelsea were determined to sign an extra forward in the summer but failed to lure Romelu Lukaku away from Everton, or Alvaro Morata from Real Madrid, and have yet to convince Swansea City to allow Fernando Llorente to make a January switch.
Brendan Rodgers is ready to play hard ball with Chelsea over any potential move for Dembele, while the player himself is thought to be enjoying his football at Celtic Park and not in any rush to leave the club.
Chelsea are one of many clubs to have sent scouts to watch the runaway SPL leaders this season and are interested in completing a more imminent deal for goalkeeper Craig Gordon as they look to replace Asmir Begovic who has an offer from Bournemouth.