A High Court hearing is due to start in January following a series of claims and counter-claims after alleged construction faults saw the scheme bust its budget.
The council’s cabinet will meet next week to decide on its approach to the mediation phase of the case.
Cllr Noel Kavanagh, the deputy leader of the council’s opposition Labour group told the Cambridge News it may be time to call a truce.
He said: “The council should come to an agreement with Bam Nuttall rather than trying to fight it out in court because the only benefits from that would be the lawyers and I would have thought the cabinet would be trying to save as much money as possible.
“There comes a point where you have to negotiate an agreement which is satisfactory to both sides and it sounds as though it would be sensible for the cabinet to come to an agreement because the courts could go against the council and leave the council with a high bill.”
At the heart of the dispute is whether the council should pay Bam Nuttall the £87m fee which was originally agreed, or the £161m the company says it spent.
If the council lost all of its case the total cost of the project could soar to nearly £230m – leaving the authority facing a £100m bill.
A council spokesman said: “The county council remains confident of its position in regard to the outcome of the contract dispute with Bam Nuttall.
“Mediation is a routine requirement for this kind of legal proceeding which is undertaken by the parties for the purposes of achieving an early settlement and this cabinet discussion will seek to finalise the county council arrangements for taking a full and informed part in the mediation discussions.”
A Bam Nuttall spokesman said it was unable to comment because of the ongoing dispute.