The new school is expected to take on 240 learners, all aged between 16 and 19, and could eventually hold 400 students.
Leeds Building Society had operated from the site in Albion Street since 1930, but announced plans in 2018 to move all of its 900 head office staff to Sovereign Street.
According to a report from AHR Architects, the new Leeds Mathematics School would help "transform opportunities" for "highly numerate young people" in Leeds and beyond.
It added: "At the heart of its work will be a focus on raising the participation of under-represented groups, especially girls and the disadvantaged, in the study of mathematics."
Developers said the new school will have 28 members of staff, and at least eight teaching areas.
An application submitted to Leeds City Council seeks permission for a change of use, refurbishment and remodelling of the building, with ground floor units to form the specialist mathematics school.
All students who attend will initially study a four A-Level programme including A-Level further mathematics and A-Level mathematics. A-Level physics, chemistry, and computer science will also be available as optional subjects.
The new Leeds Mathematics School, which is a partnership between the University of Leeds and the GORSE Academies Trust, is also a member of the UK Maths Schools Network - a growing group of specialist sixth forms which focus on the excellence in mathematics related subjects for 16-19 year olds.
Comments on the plans can be submitted until Friday August 22.