The final cost of the Third Don Crossing could be over budget by more than £2 million.
Aberdeen City Council’s finance chief Willie Young said the scheme was heading for millions over the £18m costs.
And senior city councillors have also warned the authority could be forced to take legal action against developers Balfour Beatty if there are any further delays to the project.
The bridge was meant to be completed by this month, but has been delayed.
The date was pushed back to the middle of next month, but a council report has now raised serious concerns over both the final cost of the development, and also whether the scheme will be finished in time.
The strategic infrastructure and capital plan states there is a risk the bridge will not be up and running as planned.
Finance convener Cllr Young said the project could eventually cost “anything upwards of £2m” more.
And he refused to rule out legal action if the problems with the development are not overcome.
He said: “Where we find that Balfour Beatty haven’t fulfilled their contractual obligations the council should make use of the contract that we entered into with them, but it would have to be done justly.”
Balfour Beatty said completion of the project had been severely impacted by uncharted utilities along the length of Tillydrone Road, Tillydrone Avenue and the St Machar Drive junction.
Under the terms of its contract, uncharted utilities are not the fault of Balfour Beatty and so it was awarded an interim extension of 13 weeks. A further extension is being considered to take account of the recent issues.
The project remains on target for a late Spring completion, the firm added.