Architects Hawkins\Brown and Schmidt Hammer Lassen are designing the futuristic-looking building that will replace the current library at All Saints on Oxford Road.
If the planning application is approved, work will start next summer with full completion by 2028.
As well as space for students, the building would be home to the Manchester Poetry Library and would also house a new gallery and event space for both public and university use.
Professor Karen Moore, chief operating officer at Manchester Met, said: "As an ambitious University, we are committed to providing a truly modern campus here in the city centre for our students, colleagues and the community.
"The new library will reimagine what a university library can offer and will build on Manchester Metropolitan University's rich 200-year history of education and research."
Source; Construction Enquirer