Chelsea said in March expanding their current home, Stamford Bridge, made no economic sense, while a new stadium on the site faced planning problems.
The club added they are not the only party interested in acquiring the site.
Stamford Bridge problems
- Access issues prevent development beyond 50,000 seats
- Attempts to sell naming rights stalled with Chelsea asking for £100m for a 10-year deal
- Previous attempts to sell naming rights to existing stadia have rarely been successful
"There is no certainty we will be successful," read a club statement."We must also stress that making an offer for the Battersea Power Station site does not mean the club has made a definitive decision to leave Stamford Bridge."
The club say the plans, which would preserve the building's Grade Two listed turbine hall and control room, would provide "a unique architectural backdrop to a world-class stadium".
A development of shops, housing and offices, and a contribution to the extension of the Northern Line underground service into the area, are part of the offer.
Stamford Bridge's capacity of 42,000 compares unfavourably to Arsenal's Emirates Stadium, which holds 60,000, and Manchester United's Old Trafford ground, which has seating for 76,000.
Chelsea have been linked with other sites in south-west London while they are also considering ways of increasing revenue, such as selling naming rights to their current home at Stamford Bridge.
The possibility of Chelsea relocating from the stadium they have played at for 107 years has been complicated by a disagreement with Chelsea Pitch Owners (CPO), a fan-owned company who acquired Stamford Bridge's freehold in 1997 to protect it from developers.
The club's attempt to buy the freehold back in October was rejected by CPO's shareholders, who accused it of not making enough of an effort to remain at Stamford Bridge.
Tim Rolls, a CPO shareholder, said it was his preference "and the preference of a lot of Chelsea fans is to stay at Stamford Bridge".
"That hasn't changed. I am still not convinced the club have exhausted every possible avenue for redeveloping our ground, I just don't believe they have," he added.