American superstar Prince played a surprise secret set at the club in 1995, hours after dazzling in front of 10,000 fans at the city’s SECC.
Boyband One Direction played there in 2010, while the likes of Biffy Clyro and Kasabian also headlined there before making it big.
MacLeod said the venue’s gig diary was “full up” for the rest of the year.
In a sales brochure, CDLH describe it as a “a cornerstone of Glasgow’s vibrant music scene.”
Peter Darroch, of CDLH, added: “The Garage is a truly landmark venue with a reputation that extends far beyond Glasgow.
“Opportunities to acquire assets of this stature are rare, and we anticipate strong interest from a range of buyers seeking to build on its established legacy.”