Olympic bosses have opted not to move the 2012 basketball and equestrian events, but may move badminton, handball and rhythmic gymnastics.
London 2012 organisers decided on Wednesday to go ahead with a 12,000-seater, £60m temporary arena for basketball in the main Olympic Park.
Equestrianism will stay at Greenwich Park after a review by accountants KPMG said no saving would be made by moving.
But changing the other venues could result in savings worth £40m.
London 2012 said in a statement: "The KPMG review showed that there are no significant savings to be made from moving the [basketball] venue off the park to an existing permanent facility.
"This is due to the resultant costs of venue hire, operating costs and the loss of ticket revenue due to a reduction in capacity - not building a temporary venue would significantly reduce the number of spectators that would be able to watch the event."
An alternative location for equestrian and modern pentathlon would not result in lower costs than Greenwich Park
London 2012 statement
London 2012 chief executive Paul Deighton told the London Assembly it "did not make economic sense" to move the basketball venue, which will also host the handball final and semi-finals, wheelchair rugby and wheelchair basketball, and will act as a holding area for athletes before the opening and closing ceremonies.
But he said they would look at a new venue for badminton, handball and rhythmic gymnastics away from north Greenwich.
"The draft conclusion of the KPMG report is that there ought to be an economic opportunity to shift that to save money," said Deighton.
None of the alternative venues for the equestrian events were close enough to accommodate the modern pentathlon show jumping event which needs to be located close to the Olympic Park to allow the completion of all five events within one day.
Other sites would also require accommodation for competitors as they would not be within International Olympic Committee guidelines for travel time from the Olympic Village.
"Given these considerations, an alternative location for equestrian and modern pentathlon would not result in lower costs than Greenwich Park," added the statement.
Fencing and volleyball have already been moved to existing permanent sites as the government is under pressure to keep costs down after the Olympic budget spiralled from an initial estimate of £2.4bn to £9.3bn.
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