The Crosthwaite family - parents Lucinda and Nicolas, plus children Louis and Rose - have lived in Stamford Cottages, just a goal kick away from Stamford Bridge for 50 years.
With London teams' Tottenham redeveloping White Hart Lane and West Ham moving into the 57,000 Olympic Stadium, this is a much-needed desire for the club.
Chelsea contend that the land on which the property is situated can be compulsorily acquired by the council and the injunction overridden if Hammersmith and Fulham conclude that the project would benefit the economic, environmental or social wellbeing of the area.More news: Trump Lawyer Files Pointless Lawsuit Against Buzzfeed
A three-bedroom property on the same street as the Crosthwaites sold for £1.18m previous year.
Chelsea have told the council they will be unable to start development work or secure financing while there remains a risk that the injunction proceedings could succeed.
Chelsea's offer of legal advice worth £50,000, and further compensation understood to be in the region of a six-figure sum could not persuade them to waive their "right to light" in their home.
Therefore the council plan to use their powers under planning law to buy the air rights over part of Stamford Bridge and the railway line which sits between the stadium and the affected homes.More news: Supreme Court will weigh letting states collect tax on e-commerce sales
Hammersmith and Fulham city councillors are set to meet on Monday to make a decision on what will happen next.
"The club has been in discussions with the owners of 1-2 Stamford Cottages for some time to acquire their rights to light by agreement, but they have confirmed that it is highly unlikely that a private agreement will be reached", wrote Chelsea in a report to the local councils.
Despite, the tremendous 97.5% of support coming from 13,000 local residents as well as the Major of London Sadiq Khan's approval, the Blues face a hurdle in their bid to build the most expensive European stadium.More news: Meghan Markle's final Instagram posts revealed