Designed by Ian Simpson Architects, the building will provide 343,000 sq ft of offices at Quay House and a top floor skyline restaurant.
The City Council is expected to give its verdict on the high-rise office plan on 10 April.
The application comes as Allied London have just got the go-ahead for The Cotton Building, a 10-floor multi-use development for Spinningfields on a site opposite RBS.
Michael Ingall, chief executive of Allied London said: “No 1 Spinningfields will be the district’s most imposing building to date and one of Manchester’s most stand-out office buildings.
“Our last significant building, 3 Hardman Square, won several awards for its design and specification and we expect this building to take the mantle of the best regional office building in the UK.
He added: “We have taken inspiration from buildings around the world and aim to deliver highly desirable office space combined with the city’s highest restaurant.”