Councillors are to meet behind closed doors in the Borders to discuss a permanent home for the artwork, with a town centre site in Galashiels, and a location in Tweedbank the two choices.
Both sites have been described as ‘viable options’ but the Scottish Borders Council said a report on the project would be considered in private due to ‘commercially sensitive’ information contained in it.
It is thought that the Galashiels location could attract more funding, despite Tweedbank having looked like the favourite at one point.
Council leader David Parker told the BBC: “We are proposing that we proceed to look in further detail at the Galashiels option as this may attract further additional funding that the Tweedbank project could not access and it would also act as a significant town centre regeneration project.
“Siting the visitor centre in Galashiels town centre would have the potential to unlock substantial benefits for the town, including transforming it into a true visitor destination, which could encourage further positive developments in the town over a number of years.”
However, a final decision won’t be made for some time, with a revised report scheduled to be brought back before the council in November if councillors decide to progress with the Galashiels site.
The new report is expected to focus on phasing, funding sources and further project details.
The Great Tapestry, of Scotland comprises a number of embroidered panels showing scenes from Scottish history from 8500BC until 2013, when it was launched.
The tapestry was the brainchild of author Alexander McCall Smith, who proposed a Scotland-wide tapestry after viewing the Battle of Prestonpans Tapestry.