Battersea Power Station could be left with just one of its landmark chimneys during refurbishment, under plans considered by Wandsworth Council.
Current rules state only one chimney at a time of the 1933 building can come down during the rebuild.
The Malaysian group carrying out the £8bn redevelopment said working on three chimneys together meant the project could finish two years earlier.
The group pledged to pay the full value of the chimney work before starting.
Work on the 39-acre site in south London is expected to begin in October and £100m will be spent on demolishing and rebuilding the four chimneys of the Grade II listed building, the steel frame, wash towers and brickwork.
'Speeding up' work
The site will be redeveloped into 3,500 homes, offices, shops and a park.
Battersea Power Station Development Company, which is carrying out the work on behalf of the Malaysian consortium, is calling for a "deed of variation".
It said there was "no question" of the famous structures not being replaced and it would rebuild one chimney first before starting work on the three others.
A spokesman said: "It is simply a case of speeding up the scheme.
"If we do them one at a time it would take a lot longer. If we do one and then three it's a lot quicker.
"There is an absolute commitment on behalf of the developer to rebuild the chimneys to the same design as the originals."
The council said the current legal requirement was put in place to deter developers from taking down the white chimneys and not replacing them if the development did not go ahead.
On the proposal for a bond a spokesman for the council said: "The council could use this bond to pay for the completion of the project if for any reason the developer failed to finish.
"Council planners are now examining the application in detail.
"A final decision on whether to approve the proposals will be made by the council's planning applications committee."
A decision on the proposal will be in made by August, the spokesman said.