Civic leaders in the city have put together the bid to ministers after trying to get cash for the ambitious project for more than year.
They were left disappointed when a round of funding awarded earlier this year fell short of the £50m that had been hoped for.
It is hoped the fresh application will allow the City Learning Quarter, on the corner of Garrick Street and Bilston Street, to be built.
Stuart Anderson, MP for Wolverhampton South West, said: "I am delighted to support this bid to the Government’s Levelling Up Fund.
"As a local MP, I have been calling on the Government to ensure that young people in our city have access to excellent education, training, and employment opportunities which equip them with the skills needed to lead fulfilling lives.
"If successful, the funding will help to realise the delivery of this shovel-ready project and it will make a massive difference to everyday life through direct investment in skills and education. It will be transformational for young people, residents, and communities in our city."
The purpose-built education facility will be set over 10,000sq m and will provide a state-of-the-art learning environment for young people and adults in the city and pave the way for Wolverhampton College to move from its outdated Paget Road site, which has been identified as land to build much-needed housing.