The complex wave-shaped venue, designed by Zaha Hadid, needs the extra cash to deal with problems encountered in the roof construction, and to meet strict poolside air temperature guidelines.
Balfour Beatty is main contractor for the scheme, which has already been extensively redesigned, and is now estimated to cost £268m to complete – well above the original £75m projected.
However, savings made elsewhere in the Olympic construction programme could see a final overall budget underspend of up to £500m.
The overall Olympic bill is expected to stay within the £9.3bn budget, with the share of the Olympic Delivery Authority (ODA), which manages the construction phase, expected to come in at £7.23bn.
But the final cost will still be considerably more than the estimated £2.4bn announced when London successfully bid to host the Games.
A performance-related payment of £10m has been put aside for the ODA's delivery partner, Laing O'Rourke's CLM consortium.
"The ODA has continued to drive down costs and deliver savings despite this being the most complex year in construction terms," said Olympics minister Hugh Robertson.
The ODA has made £750m of savings since the 2007 baseline budget was agreed, including £29m in the last quarter.
This included £7m saved by ditching the distinctive plastic wrap around the main stadium.
"As soon as we were clear that this wouldn't affect wind speeds and timings in the stadium then we were happy to take the wrap off and then open it up to architectural experts and others who will take a view, and indeed sponsors, and the private sector in general to see if they want to have a look at it," said Robertson.