The Blues' ownership is looking to expand the capacity of Stamford Bridge, currently set at 42,000, in order to accommodate more fans.
However, any work on the stadium is expensive and involves a great deal of hurdles.
The source adds that Chelsea have held discussions with Transport for London (TfL), one of the partners that manages the Earls Court site.
They have drawn up plans and have even identified the Lillie Bridge depot as the area where they can build the new stadium.