It is reported that private equity group Patron Capital, led by ex-Lehman Brothers banker Keith Breslauer, is the new frontrunner to buy the firm.
Several other private equity groups and Taylor Wimpey had previously been linked with Cala as potential buyers.
More than 137 years ago, Cala was the first Scottish company to be listed on the London Stock Exchange. In 1999, it was taken private by its management team, then led by Geoff Ball, with the backing of Bank of Scotland.
After the 2008 housing crisis, Lloyds Banking Group took a 32% stake in the firm following a £280m debt for equity swap.
Management and staff, which own the rest of the house builder, could be in for a major windfall, with forecast valuations as high as £250m.