Billionaire owner Roman Abramovich is believed to be keen on the switch so he can fund a new 65,000-seater stadium, replacing their current 42,000-capacity Stamford Bridge home, reports BBC Sport.
A lack of space has prevented Chelsea increasing its current capacity.
The Earls Court and Olympia complex are owned by St James Capital and they have "received approaches" according to a spokesman.
Rivals Manchester United will soon be playing in front of 75,000 at Old Trafford and Arsenal move into their new 60,000 stadium at Ashburton Grove next season.
St James' entrepreneurs put the Earls Court and Olympia site up for sale in December for £400million.
The entire site takes up around 36 acres, with Abramovich looking for 13 acres on which to build any potential new ground for Chelsea.
The Blues could then sell Stamford Bridge, which may be worth up to £500million.
