Critics have claimed Shropshire Council is "living in cloud cuckoo land" for thinking it could build it for £81m when the Pant-Llanymynech bypass, a shorter road, could cost £378m.
Bosses are remaining tight-lipped on how much they now think the four-mile Churncote to Battlefield road will cost for "commercial confidentiality" reasons, but said it is "fair to assume" the road will cost more than had been anticipated due to rising costs throughout the economy.
A Shropshire Council spokeswoman said: "We expect that a planning application for the North West Relief Road will come to planning committee as soon as possible in the autumn and the date for this will be publicised in advance of this meeting.
"The full forecast cost of the NWRR (including Oxon Link Road), subject to planning approval, would then be set out in a paper to councillors around the end of the year to agree the submission of the full business case to the Department for Transport.
"Given rising costs across the whole economy and in particular the construction industry, it is fair to assume the scheme’s cost will inevitably be higher than the roads original budget.
"However having just completed a financial review of the scheme with a number of key contractors and the supply chain, we remain confident that this will be financially viable for the Council and we are looking at a range of ways that any increase in budget can be met while minimising any extra financial burden on the council.
"The full business case will describe the value of, and approach, through which our own match funding requirement will be delivered.
"To ensure that the council achieves the best value from bidders for the contract to deliver the NWRR, we cannot for reasons of commercial confidentiality divulge more details until the contract is let. These figures would move into the public domain and open to scrutiny by the council at that point as part of the full business case process."
The £81 million estimate is based on 2017 prices. Better Shrewsbury Transport campaigner Mike Streetly described the numbers, given the current climate, as "total fantasy" and said the estimate "belongs in cloud cuckoo land".
The project has been heavily criticised, with more than 4,500 objections being lodged on the planning application. However council bosses think it will help improve Shrewsbury as somewhere to visit, slash pollution in the town centre and benefit surrounding towns and villages.