Delays mean the controversial Norwich Northern Distributor Road will not be fully open before Christmas.
However, drivers could be using some sections of the £178.5m road before the year is out, if traffic modelling shows that would not heap pressure on existing roads.
And Norfolk County Council and its contractors will need to thrash out agreement over how much the delays and design changes have added to the bill.
The council and contractors Balfour Beatty had hoped the 12.5-mile dual carriageway road, stretching from the A47 at Postwick to the A1067 Fakenham Road, could fully open by the end of the year - three months ahead of the initial timetable.
But delays and design changes at the eastern end of the road, connected mainly to difficulties in getting the go-ahead from Network Rail for the Rackheath Rail Bridge, mean that looks unlikely.
Council bosses are considering opening up the sections of the road which are likely to be finished.
Tom McCabe, executive director of community and environmental services, said: 'If we had got Rackheath Bridge away than a December opening would have been viable.
'But we are looking at whether we can open sections of the road which are likely to be finished.
'There's a good chance we could get the stretch between the A1067 and the A140 and the section between the A140 and Wroxham Road open.
'We will need to do traffic modelling to see what the effect would be, because we don't want to be throwing traffic onto, say, Boundary Road.'
In September, council bosses admitted the cost of the £178.5m road could increase by £6.8m. Mr McCabe said the delays and design changes were likely to increase the figure further.
At a meeting next week, councillors will be given details of the latest figures, but the press and public will be excluded.
Mr McCabe said: 'This is the subject of robust commercial discussions between us and Balfour Beatty.
'It's my job to make the figure as low as possible. The reason we have a below the line report is there will be commercially sensitive information in the report.
'It's only right we share that with councillors, but it's important that we protect our position.'
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