Next Tuesday, March 1, members of the local authority's decision-making executive committee will be recommended to allocate the monies from its Second Homes Council Tax funding budget to enable Selkirk-based Eildon Housing Association to go-ahead with the development.
If agreed it would be the second time the council has contributed towards the cost of the project - after a £250,000 grant in 2017.
The latest shortfall has come about because of costs involved in having to relocate an adjoining business and increased tender prices.
The council's long-term housing strategy identifies the redevelopment of the old school site as a priority.
A report to next week's committee says: "In 2017, the council previously paid a £250,000 transfer from the Second Homes Council Tax budget to the council's capital budget as a contribution towards meeting the market valuation of the site through the sale of the site to the Association.
"However, in the context of the delays to the original project programming, negotiating the relocation of an adjacent business, continued increasing tender prices and despite efforts to make savings, a funding shortfall of £512,000 has been identified."
In response to that shortfall the Scottish Government has agreed to contribute an additional grant of £312,214.
The report adds: "Despite this there is a remaining funding gap of £199,868. It is proposed the council grant up to £200,000 to gap fund the project to enable it to progress.
"It is considered that the proposed council grant contribution of up to £200,000 is an appropriate use of the available Second Homes Council Tax balance and is consistent with the published Scottish Government regulations which frame eligible uses of this funding."
The former school closed several years ago and the site cleared with a new high school opening in the town's East End back in 2009.