The club has appointed a developer to explore the feasibility of building at the site which has been empty for years.
The club is acting in order to avoid missing out should the Battersea location emerge as the most viable relocation option if it outgrows Stamford Bridge.
Chelsea have appointed Mike Hussey, the chief executive of Almacantar, as development partner and have hired the architecture firm Kohn Pedersen Fox to draw up plans for the construction of a 55,000-60,000-seat stadium to the south-east of the Grade II-listed power station site.
A Chelsea spokesman said: “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 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.”
Chelsea have still not given up hope of persuading the owners of Earls Court to give them permission to build there but the prospects are fading.