The International Olympic Committee (IOC) controversially decided in July to eject both sports from the games. But voting in Singapore was so close that there is pressure from both sports' governing bodies for another ballot to be held.
Softball fell one vote short of the majority needed to stay on the programme, while baseball lost its place by only three votes.
They were the first sports to be dropped from the Olympics since polo in 1936. The IOC then rejected the opportunity to add any sports to replace them, turning down applications from rugby sevens, golf, squash, karate and roller sports.
If the sports are restored it could cost £50million to build temporary venues to host them.
However, the cost was fully accounted for when London originally submitted its bid, as this preceded the removal of baseball and softball by the IOC.
