It was awarded the contract by Fusion Group to build the 420-bed scheme, opposite the Liverpool Institute of Performing Arts (LIPA).
Work is expected to be finished by June 2025, in time for the September intake of students.
The building is within walking distance of University of Liverpool and Liverpool John Moores University, and will include a recording studio, half basketball court, fitness studio, library and zero waste shop.
McAleer & Rushe said it will deploy off-site manufacturing using light gauge steel frame structures and bathroom pods to make the building process more efficient.
It has previously built more than 11,500 units of purpose-built student accommodation (PBSA) in the UK and Ireland, with another 2,500 under construction.
Peter Devlin, contracts director at McAleer & Rushe, said: “With our extensive experience delivering PBSA schemes across the UK and Ireland, we are well placed to deliver a scheme for Fusion Group that will help to revitalise the Upper Duke Street area of Liverpool and provide young people with a high-quality student living experience. As construction partner and building on our successful early engagement approach, we are making use of offsite manufacturing to deliver benefits throughout the construction process delivering the scheme efficiently and sustainably.”