The scheme, which Shropshire Council says will reduce traffic in the town centre, was originally forecast to cost £71m, on top of the £12m Oxon Link Road.
Now merged into a single project, with an increased total budget of £87.2m, it is expected that a planning application will be submitted in February next year.
The application has been delayed while consideration is given to including a water retaining embankment or dam in the designs to prevent flooding.
But a report published ahead of a council meeting next week warns the current cost estimate has risen to £95.7m, based on the worst case scenario. The best case scenario, it says, is an underspend of £5.9m.
The planned route will connect the A5 at the Welshpool Road roundabout in the west to the Ellesmere Road roundabout in the north, with new bridges over the River Severn and the Shrewsbury to Chester railway line.
The report, by Matt Johnson, strategic projects executive manager, says: “Estimated risk items currently still include construction phase risks and required utility diversions.”
It also reveals the council had already spent £5.8 million on designing and planning the road by March this year.
The report says: “At this stage of a project of this nature, it is to be expected that there remain unresolved cost items, pending further investigation and design leading to increased cost certainty.
“It should be noted that all remaining estimated costs are based on a reasonable worst case scenario, and that appropriate construction and client side risk allocations – of a value appropriate for such a project – remain in place to offset such matters until such time as cost certainty is in place.
“Full cost certainty at the time of the full business case and construction contract award will be required before a decision is taken to proceed.”
Campaigners fighting for the project to be abandoned have said the latest figures show it will be a “financial disaster”.
'Financial disaster' - campaigners
Steve Hale, from the campaign group Road to Ruin Shropshire, said: “The eye-watering sums of Shropshire money being spent on the North West Road are proof that this project is a true road to ruin and a financial disaster for Shropshire.
“The council has already spent £5.8m on consultants while it has dithered, delayed and changed its mind about what it’s actually trying to build. Meanwhile, the projected costs keep getting higher and higher.”
The relief road has attracted grant funding of £54.4m from the government, leaving the council to pay the remaining £19.8m – plus any overspend.
The Oxon Link Road will be funded by a £4.2m grant from the Marches Local Enterprise Partnership (LEP) and money collected from developers through section 106 agreements and community infrastructure levy payments.
Mr Hale said: “People we speak to tell us they’re desperate for cycle lanes, electric buses, local investment after years of austerity, and better maintenance of Shropshire’s existing, pot-holed roads.
“These are all things that could be financed if the road was cancelled.
“But our biggest concern is that Shropshire is solely responsible for 100 per cent of any overspend.
“Do we really want to be on the hook for millions of pounds more than we’ve budgeted for just as unemployment soars and we’re struggling with a global pandemic?
“It’s financial insanity, worse even than the purchase of shopping centres which have already been devalued to the tune of £17 million since they were bought. Not a great track record in spending our money."
Shropshire Council has been contacted for comment.