The club have asked a London developer to look into the feasibility of the scheme so that they will be ready to move if Battersea Power Station seems like their best option.
Chelsea need to buy back the freehold of Stamford Bridge before they can move and they are also considering relocating to an area next to Earls Court.
However Battersea Power Station is fast emerging as a likely contender for the new football ground.
A Chelsea spokesman told the Press Association: “In the past, we’ve talked to various people with interests in Battersea Power Station, but we haven’t had any substantive discussions with anyone regarding that site for several months.
“However, in light of current developments, we now think it prudent to look again at the feasibility and potential for the BPS site to be developed for a football stadium.
“We have made no decision to leave Stamford Bridge, and we continue to discuss with the local council any economically viable options to expand the Bridge, but we will continue to investigate various options close to Stamford Bridge.”
If the move does happen, Chelsea would be unable to make radical changes to the appearance of the Grade II listed. The stadium, if it was built, would be next to, or inside the current structure.