Chelsea has been looking for a new playing ground after deciding it would be difficult to expand its existing facilities at Stamford Bridge where issues of access has prevented development beyond the current 50,000 seats.
Executives at the club have indicated they would like to redevelop Battersea Power Station into a 60,000 capacity stadium.
The landmark building, which is famous for its four chimneys, has a grade two heritage listing.
Chelsea club management indicated it would retain the building's character if a sale should go through.
Chelsea, which has also been linked with other sites in south-west London, has said no definitive decision has been made to leave Stamford Bridge, which is only a short distance from the power station.