The Blues announced they and property development partner Almacantar were hoping to acquire the 39 acres of land they could redevelop if they decide to relocate from Stamford Bridge.
The clubs plans include preserving all the significant aspects of the power station itself.
Chelsea said in a statement: "Battersea Power Station is one of London's most famous buildings and has the potential to become one of the most iconic football stadiums in the world.
"Our joint bid was submitted in accordance with the sales process established by the joint administrators for the site. The process could run for a number of months.
"We are not the only interested parties and there is no certainty that we will be successful."
Chelsea cannot move from Stamford Bridge unless they can convince fan-led group Chelsea Pitch Owners, who own the land beneath Stamford Bridge, to sell them back the freehold.
That was something they failed to do at an extraordinary general meeting of CPO back in October.
The statement added: "We also appreciate that we have many significant hurdles to address if we are to build a new stadium on the site, including winning the support of our fans, the CPO shareholders and local Wandsworth residents, as well as securing the approval of Wandsworth Council, the Greater London Authority and heritage authorities.
"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.
"Working with architects and planning experts, we have developed a plan to preserve all the significant aspects of Battersea Power Station.
"The four iconic chimneys and wash towers along with the Grade II* listed west turbine hall and control room will be restored and retained in their original locations and provide a unique architectural backdrop to a world-class stadium with a capacity of around 60,000 seats.
"Following feedback from fans, our initial plans include a 15,000 all-seated one-tier stand behind the south goal, likely to be the biggest one-tier stand in football.
"Also as suggested by many fans, the stadium proposed is rectangular in shape with four separate stands. The design includes a bigger family area and more room for disabled supporters.
"As well as a new home for our club, the development would include a town centre with substantial street-level retail shops, affordable housing and offices - all of which would benefit Wandsworth and bring a significant number of permanent jobs to the area.
"We would also make a significant contribution towards the Northern Line Extension, a new high-volume transport link proposed for the area.
"We will keep our fans updated as the process develops."