Hammersmith and Fulham Council have refused to concede defeat in their attempt to keep Chelsea at Stamford Bridge, despite the club confirming they had submitted a bid to transform Battersea Power Station into a new stadium.
The Blues on Friday announced plans to turn the Grade II* listed building in Wandsworth into "one of the most iconic football stadiums in the world".
A 60,000-seater ground, which would take between three and four years to construct, would include the power station's four chimneys and other aspects of the existing structure as part of the design.
Chelsea maintain they have yet to decide whether to relocate but they have also insisted it is not economically viable to redevelop Stamford Bridge.
That has been disputed by Hammersmith and Fulham Council, whose deputy leader, Nick Botterill, said: "We want the Blues to stay at Stamford Bridge and - if it can be done sensibly without negatively affecting local people - increase the ground's capacity so they can retain their position as one of Europe's top clubs.
"CFC is a thriving business which contributes significant benefits to the area and we will continue to work closely with the club to explore all possible avenues for keeping them here at their original home."
Chelsea's hopes of moving rest on convincing fan-led group Chelsea Pitch Owners to sell them the freehold of their current home, something they failed to do at an extraordinary general meeting in October.
SayNoCPO, the group of CPO shareholders who spearheaded the opposition to their bid six months ago, said: "The viability of redeveloping Stamford Bridge is still a very relevant issue, with Hammersmith and Fulham Council openly contradicting the club's negative projections."
It is understood Wandsworth Council have no objection in principle to a football club bidding for Battersea Power Station.
Chelsea are not the only bidders for the 39-acre site, which was valued at £500million in October and was put up for sale two months later amid an adminstration saga.
The Blues 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 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."
Any new stadium is likely to contain four separate stands in accordance with the wishes of Chelsea's fans, with a 15,000-seater single-tier south stand.
The club have also offered to contribute to the cost of a planned extension to the Northern Line into the area.