A spending timeline until 2022 shows the price could be about £435,000 more than approved in the Scottish Borders authority's budget earlier this month.
The Scottish government contribution to the project has been estimated at about £32.5m.
The council is being asked to approve the final outline design of the scheme and aim to publish it in April.
A report to the local authority described publication as "the most important stage of the project for determining the programme and successfully obtaining funding".
It warned that if the objection resolution process went beyond an estimate of three months, it could put funding at risk as well as the delivery target of June 2021.
However, the project team has tried to avoid that prospect with extensive consultation over the past two years.
A council report has shown the total estimated costs of a flood protection scheme for Hawick could top £41m.