The restaurant chain said they received 4000 applications in one day after the recruitment drive to find 80 staff launched on Monday.
As reported in the Evening Times, cafe bosses are looking for employees who are friendly, hard-working and with a big personality.
Potential employees also have to be music lovers and be passionate about Glasgow.
The venue, in the A-listed former Athenaeum Theatre near the top of Buchanan Street, is currently being renovated and will open its doors in mid-November.
Debbie Galbraith, director of European human resources for Hard Rock, said the firm was "absolutely overwhelmed by the response".
She added: "In 24 hours, we have received 4000 applications.
"It's amazing that so many great people in the city want to become part of the Hard Rock family.
"Glasgow has such a rich heritage and is a fantastic music hub that we knew the Hard Rock brand would fit perfectly in the city."
Glasgow's Hard Rock will seat 170 diners and showcase pop memorabilia, including a green two-piece suit worn by The Who's Pete Townsend and the Epiphone Firebird guitar that singer KT Tunstall used in her Hold On video.
The new recruits will join a global workforce of 39,000 Hard Rock staff working in venues across more than 50 countries.
Marc Carey, Hard Rock European marketing director, said: "We need 80 passionate, hard working, rock 'n' roll people to join the Hard Rock family in Glasgow and already we have 4000 people wanting to do this.
"We knew that opening a cafe in Glasgow would be a fantastic opportunity not only for the brand but for people in the city too.
"For us, Glasgow has such a great variety of people and holds such a strong musical history that we hoped the city would welcome Hard Rock and the response to the recruitment drive speaks volumes."
Other exhibits going on show at Glasgow's Hard Rock include a velvet schoolboy outfit worn by Angus Young, the Glasgow-born AC/DC guitarist, and an artist's palette used by the 'fifth Beatle', Scottish-born bassist Stuart Sutcliffe.