Construction on the transport scheme went £64m over the original £87m budget.
And now both sides could be heading to the high court to fight over who picks-up the bill if they fail to reach a mediated settlement following a string of problems on the contract.
Cambridge-news.co.uk said a county council cabinet meeting has authorised the start of legal action in the Technology and Construction Court.
Cllr Ian Bates, the council’s planning chief, said: “The council is taking all necessary advice to resolve the dispute and will not take rash action to jeopardise taxpayers’ money.”
The council said it will still try to reach a mediated settlement despite the authorisation of legal action.
It believes it owes Nuttall the £87m original fee plus any differences for delays and alleged defects.
Nuttall said the project cost £151m to build and wants full payment.
The council expects the cost of the legal battle to be about £6.5m and a spokesman said this money was set aside as part of the busway budget.