Blues chairman Bruce Buck and chief executive Ron Gourlay said that the club had still to decide whether to move to a new home but insisted they would not be able to do so unless they regained ownership of the pitch and stands at Stamford Bridge.
Those currently belong to a company called Chelsea Pitch Owners, which was formed in 1993 to prevent the stadium falling into the hands of property developers.
The threat of Chelsea being made homeless subsided when Roman Abramovich bought the club but they are now unable to move from Stamford Bridge unless they can profit from the land it sits on.
On Monday, Buck and Gourlay appealed to the 12,000 CPO shareholders - most of whom are fans - to sell their 15,000 shares to the club for the price they paid for them in return for various incentives at any new stadium.
Each CPO share cost only £100 and Buck is hopeful that supporters will not try to hold the club to ransom, insisting there was no room for negotiation anyway.
"Bear in mind that no one bought these shares as a financial investment," he said.
"Everyone bought these shares as a way of helping the club and they also bought them as mementoes and souvenirs.
"We haven't considered making them a big offer because we believe that they are fans of Chelsea Football Club and want to do what's best for Chelsea Football Club and we've offered them a couple of things relating to their role as a fan."
The incentives for selling up include a guarantee that Chelsea would only relocate within a three-mile radius of Stamford Bridge if the club did decide to move before 2020.
Buck and Gourlay could not make any promises beyond that year because the sites they would currently consider - which are understood to include Earls Court, Battersea Nine Elms and possibly White City - are likely to become unavailable during the next eight years.
CPO shareholders who vote in favour of selling up at an extraordinary general meeting scheduled for October 27 were also promised their names would appear on a roll of honour or walk of honour at any new stadium and that they would be given priority in selecting a season ticket at that stadium.
Chelsea need a yes vote from the shareholders of 50% of the shares who actually turn up to this month's EGM.
With only around 60 or 70 people attending CPO's annual general meetings, a small turnout is expected, with the club understood to be planning to book a room that holds up to 400 people.
The nightmare scenario for Chelsea is that the EGM is attended primarily by those who would want to veto the proposal, some of whom may argue Abramovich could easily afford to pay a premium on the shares.
But Buck claimed that even though the deal on offer meant no return on shareholders' investment, they were getting back far more than the land was worth - £20,000 - when the 199-year lease on Stamford Bridge was taken into account.
"We think we're paying well over the odds," he said.
A bigger stadium would help Chelsea compete financially with Manchester United, Arsenal and Manchester City.
Buck insisted the club had explored in great detail the possibility of redeveloping Stamford Bridge but that every idea put forward had proven impractical or too expensive.
He added: "I wouldn't say that we've given up but, after five or six years of looking at it, I would say that we're doubtful that we could do something at a reasonable cost."
If Chelsea do decide to move, Earls Court would appear to be their preferred site but its owners do not currently want a football stadium built there.
The club had ruled out White City but might be prepared to look at it again, while Battersea Nine Elms is understood to be another possible destination.
Imperial Wharf was also looked at but is too small, while Chelsea have not considered Wormwood Scrubs and Old Oak Common as they are too far from Stamford Bridge.