It is two weeks since the club announced their plans to repurchase the land they sold to supporter-led group Chelsea Pitch Owners in the 1990s.
The proposal, which has been seen as a precursor to a move to a new 60,000-seater stadium, has met with a mixed response from fans.
Chelsea need 75% of CPO shareholders who attend, either in person or by proxy, an extraordinary general meeting on October 27 to back their bid in order for it to succeed.
They have spent the past fortnight actively trying to encourage the 12,000 CPO shareholders to vote yes, while their opponents established a campaign last week called 'Say No CPO' (SNCPO).
Representatives from the campaign have met twice with Chelsea chairman Bruce Buck to plead their case and today saw them make a counter-offer to the club.
Chelsea's proposal included a promise not to move outside a three-mile radius of Stamford Bridge before 2020, after which date they believe all suitable sites in that area would become unavailable.
Some have cast doubt on whether the club would adhere to that promise and SNCPO today said they would be happy for the Blues to have "total freedom to move to a larger new stadium anywhere within three miles of Stamford Bridge at any time before 2030 so long as Roman Abramovich is still in control of Chelsea".
Chelsea's commitment to remaining within three miles of their current home appears to be supported by documents which show they have actively lobbied Hammersmith and Fulham Council to ensure both Earl's Court and White City could have a new stadium built there.
SNCPO have also demanded that the current CPO set-up be transferred to any new stadium, saying today they would encourage shareholders to sell up if the club did so.
Buck explained on Friday that because Chelsea was now worth more than any site on which a stadium would be built, the existing arrangement was completely redundant.
SNCPO also demanded that the club "agree to ongoing consultation, and transparency of information, with the fans regarding any new stadium".
A spokesperson for the campaign added: "All fans appreciate what Roman has done, so we are willing to try to meet the club with a proposal that should be reasonable to both sides and are open to discuss other options.
"The club can trust CPO shareholders to act responsibly to discussions about this issue, we await with interest the club's response.
"'Say No CPO' are happy to meet the club at any time to discuss this further."
But a Chelsea spokesman said in response: "We have made what we believe to be a reasonable proposal to the CPO shareholders, and that is the proposal that will be put to them on October 27.
"We have been discussing our proposal with shareholders and supporters groups and we will continue to do so."