The burger chain has lodged an application to convert the former Yorkshire Building Society premises opposite Piccadilly Gardens into a restaurant.
Under plans lodged with Manchester City Council, Five Guys would occupy the basement and ground floors of the five-storey building.
Yorkshire Building Society will vacate the grade-two listed property at the end of this month when it relocates to 36 Cross Street.
Firstplan is the planning consultant and Blacksheep is the architect for the Five Guys project.
Elsewhere in Manchester, the chain has restaurants in the Arndale, on Oxford Road, and at Parrs Wood Entertainment Centre.
The first UK Five Guys opened in July 2013 in Covent Garden in London, since then Five Guys has expanded, opening 113 restaurants throughout the UK.