"It is clear to the board a complete new build of a 60,000-seat stadium has little chance of acceptability," the 2010 Premier League champions said on their website.
"We believe that, after discussions with the local council, they have [also] come to the same conclusion.
"A 60,000 new-build would cost over 600 million pounds and require the club to play away from home for at least three seasons and, even if the economics were acceptable, the planning risks would likely be insurmountable."
Among the obstacles for an expansion to the stadium are two conservation areas to the south and east and the fact Stamford Bridge is bounded by railway lines on two sides.
There are also several listed buildings close by, a cemetery to the east containing listed monuments and a number of residential properties adjacent to the site.
Chelsea made a proposal to buy the freehold of their 107-year home last year to clear the way for a possible stadium move but it was rejected by Chelsea Pitch Owners (CPO).
CPO was set up in 1993 when the now mega-rich club were in financial difficulties and the fan group acquired the freehold of the pitch to protect Stamford Bridge from developers.
The ground's existing capacity is 42,000 and Chelsea said on Friday that an increase to 55,000 would also be difficult.
"The cost per seat of expanding the stands [to a 55,000 capacity] is very high," the club said.
UNSATISFACTORY RETURN
"The incremental revenues provide an unsatisfactory level of return, would not even cover the hypothetical financing costs, and the planning risks are significant. We believe the council recognises these challenges.
"The club [however] are not in any way stating we have made a decision on the need to move."
In November, Hammersmith and Fulham Council pledged to try to help Chelsea remain at Stamford Bridge and to examine ways of expanding the ground.
The London club feel the 42,000 capacity puts them at a financial disadvantage compared with Premier League rivals such as Manchester United (76,000) and Arsenal (60,000).
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 nine years ago.
Chelsea also reached the 2008 Champions League final.
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