Rival KKR was believed to be close to sealing a deal with fellow private equity firms Cinven and CCMP Capital Advisors also in the hunt but all are now thought to be out of the running.
According to sources familiar with the sale, FTSE-listed buyout firm 3i has emerged as the lead candidate to take control.
Equistone took a stake in Audley Travel back in 2012 in a deal believed to be in the region of £90 million.
The company has experienced impressive growth over the last five years.
