A week ago the West London club said a reconstructed 60,000-seat stadium at Stamford Bridge was an unlikely prospect before adding the planning risks would probably be "insurmountable."
However, the local authority, Hammersmith and Fulham Council, believe an expanded venue is possible at the site.
"Stamford Bridge is Chelsea's historic home and the council believes it should be their future home," said deputy leader Nick Botterill in a statement.
"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.
"We cannot comment on the financial conclusions CFC (Chelsea FC) have drawn but it is very likely any move away from Fulham would cost far more than either the 600 million pounds the club claim it would cost to rebuild their ground or the cost of upgrading and expanding the existing structures."
Among the obstacles to an expansion of the stadium are two conservation areas to the south and east and the fact Stamford Bridge is bounded by railway lines on two sides.
There are also several listed buildings close by, a cemetery to the east containing listed monuments, and a number of residential properties adjacent to the site.
"It is clear to the board a complete new build of a 60,000-seat stadium has little chance of acceptability," Chelsea said last week.
"We believe that, after discussions with the council, they have [also] come to the same conclusion."
COUNCIL'S PRIDE
Botterill, though, said the council would keep talking to the club to examine ways of keeping Chelsea at Stamford Bridge.
"We are proud to be the only borough in the country with three Premier League clubs [Chelsea, Fulham and Queens Park Rangers] and we do not want our local businesses and residents to lose out on the economic and social benefits this brings," he added.
"CFC are a thriving business contributing significant benefits to the area and we will continue to work closely with CFC to explore all possible avenues for keeping the club at their original home."
Chelsea made a proposal to buy the freehold of Stamford Bridge last year to clear the way for a possible move but it was rejected by Chelsea Pitch Owners (CPO).
CPO was set up in 1993 when the now mega-rich club were in financial difficulties and the fan group acquired the freehold of the pitch to protect Stamford Bridge from developers.
Chelsea feel the existing 42,000 capacity puts them at a financial disadvantage compared with rivals such as Manchester United (76,000) and Arsenal (60,000).
Chelsea said matchday revenue at Arsenal more than doubled when the club moved to the 60,000-capacity Emirates Stadium in North London from nearby Highbury (38,000).
Some supporters, though, were concerned Russian owner Roman Abramovich wanted to build a new stadium well away from West London and feared selling back the freehold would remove an important safety net for Chelsea.
The Stamford Bridge club have won the Premier League three times and the FA Cup three times since billionaire Abramovich took over nine years ago.
Fifth-placed Chelsea, who host Stoke City in the Premier League on Saturday, also reached the 2008 Champions League final.
