The club has has appointed a leading developer to carry out a feasibility study.
Chelsea's current home Stamford Bridge is owned by Chelsea Pitch Owners plc (CPO) – a company founded in 1993 to safeguard the London club's future at Stamford Bridge.
Chelsea would need to secure the freehold and sell that site before any switch to a new ground would become viable – but CPO rejected a recent approach by the club.
Mike Hussey, chief executive of Almacantar, has been appointed by Chelsea as development partner to explore the viability of a move to Battersea.
The architectural firm Kohn Pedersen Fox has been hired to draw up plans for the potential construction of an arena that would house between 55,000 and 60,000 spectators.
It would be situated to the south-east of the Grade II listed power station, with commercial operations such as hotels and shops to be housed within the building.
Any plans would have to be passed by Wandsworth council.
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 Battersea power station 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."
The Battersea Power Station site, owned by Real Estate Opportunities (REO), has been empty for nearly two decades. REO has been attempting to attract an equity investor for a year to fund a proposed £5.5bn redevelopment, yet the site is already saddled with around £300m of debt owed to Lloyds Banking Group and Ireland's National Asset Management Agency.
Other possible sites for Chelsea include the northern end of Earl's Court, whose owner, Capital & Counties plc, is pursuing residential and commercial developments of the site, and White City, near the home of Queens Park Rangers FC.