"In light of the recent decision by Chelsea Pitch Owners to retain its freehold of the ground, we reaffirm our desire to see Chelsea remain in the borough and our commitment to help the club remain at their historic home," the local council said in a statement.
"The council now proposes to examine whether there are planning options to expand Stamford Bridge to accommodate a larger capacity, recognising that such a project must be economically viable, benefit local businesses and not unreasonably affect residents."
Chelsea made a proposal to buy the freehold of Stamford Bridge to clear the way for a possible stadium move but it was rejected by CPO last week.
"Hammersmith and Fulham Council is proud our borough uniquely contains three Premiership football clubs, Chelsea, Fulham and Queens Park Rangers," the statement added.
"We recognise all our clubs will need greater capacity to accommodate growth in their fan bases and that new (UEFA) financial fair play rules necessitate generating extra matchday revenues to remain competitive.
"We are assisting Fulham with plans to expand the capacity of their historic Craven Cottage ground. We look forward to working closely with Chelsea and all local stakeholders ... to examine the options of redeveloping Stamford Bridge."
CPO was set up in 1993 when the now megarich club were in financial difficulties and the fan group acquired the freehold of the pitch to protect Stamford Bridge from developers.
Seventy-five percent of votes were needed to accept the football club's proposals last week but only 61.6 percent were in favour.
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).
However, some supporters were concerned Russian owner Roman Abramovich wanted to build a new stadium well away from south 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 eight years ago. They also reached the 2008 Champions League final.
Chelsea visit Racing Genk of Belgium in a Champions League Group E game later on Tuesday.