The world's longest embroidery tapestry is on a tour of the country having been unveiled at the Scottish Parliament last September.
But the team behind the project, created by more than 1,000 volunteers, want it to be housed at a new centre in Tweedbank, near Galashiels, Selkirkshire.
It has been estimated the capital costs for a building to house the 150-yard long The Great Tapestry of Scotland - which tells the nation's history in 160 intricate panels - range between £2.6 million and £5 million.
At a meeting in Hawick Town Hall the Scottish Borders Council agreed to finance the study.
Alexander McCall Smith, who thought up the tapestry, said: "I am confident that this will become one of the greatest tourist attractions in Scotland."