Howdenburgh Primary is one of the town’s three schools due to close next year.
The Lothian Road school, built in 1970, will close for good once pupils transfer to the town’s new £32m intergenerational campus at Hartrigge Park next March.
The council put the 5.6-acre site on the market last week through Galashiels firm Edwin Thompson.
But now some residents who believe the site might not be the council’s to sell are asking that the local authority come up with proof of ownership before taking any further action.
A debate has broken out on the Jethart’s Here Past and Present Facebook page, a social media page used as a forum to discuss town issues.
Postman and 1991 Jethart callant Scott Irvine said: “This land was left to the people of Jedburgh through the last will and testament of the late William A Skead.
“It may not be council land and there are stipulations on this land.
“I did a freedom-of-information request about this a few years ago and got a tip-off that Scottish Borders Council may try and sell this land, not realising that they may not own it, and keep the proceeds from it. “
He suggested if that is the case that the town’s common good fund could benefit instead.
Former town provost Richard Gordon, however, suggested: “The reason the common good fund is cash-rich is that the then trustees of the fund went to the Court of Session and got a ruling that that land could be sold for development.
“If Jedburgh Town Council sold the Howdenburn school site to Roxburghshire County Council or Borders Regional Council, then it will now belong to Scottish Borders Council, who can sell it for development if they wish.”
Mr Irvine, who says he has a copy of Mr Skead’s will, added:“I have evidence provided by the council that this land was given to Jed. It’s up to them to produce the evidence of buying it from us.”
Other townsfolk supported the idea of asking the council to prove its ownership, and others still questioned the lack of community consultation.
A cCouncil spokesperson said: “Our records show that the land is owned by the council, but further checks are being carried out to confirm this position.”
The asking price for site has not been revealed yet, but surveyor Edwin Thomspon says in its sales pitch: “The former school buildings will be demolished and cleared by Scottish Borders council prior to sale.
“The site is available with vacant possession as a cleared site in autumn 2020.
“The site is within the Jedburgh development boundary and is identified as a regeneration site.”
within the council’s main issues report which is the forerunner to the Scottish Borders Local Development Plan 2.”
Inquiries into the sale are invited to Edwin Thompson’s Galashiels office.