Watson Steel is believed to be on the brink of winning the contract, as it leads in a field of four.
The planning process for the porject, due to be sited on the south bank of the Thames, could be seriously delayed following Lambeth's decision to axe 44 of the 76 full-time planning jobs.
The cuts follow an independent report in June which said the department was in 'chaos' with a back-log of 1,130 applications. It recommended 14 redundancies.
'We are confident that planning permission for most of these projects is through. Those that are not yet through are in constant discussion and have been given the highest priority,' said a council spokesman.