Wolverhampton Council has been trying to secure funding from ministers for the Learning Quarter, which would become the new home of the city's college on the old Faces nightclub site, for more than a year.
Council leader Ian Brookfield has been left disappointed by the amount of cash that has been given to Wolverhampton so far and said the Government needed to do its bit to support the city.
A fresh bid for £20 million from the 'Levelling-Up Fund' is to be submitted.
Councillor Brookfield said he was frustrated by the Government's bidding culture which he believes pits areas of the country against each other.
He said: "With the Learning Quarter it was always going to be this way when we are living in a bidding culture.
"For some unknown reason this Government likes people to bid against each other. It's a bit strange Mr Johnson is trying to level up by areas having to bid against each other."
The education facility, which already has planning approval, will be set over 10,000sq m and will provide a state-of-the-art learning environment for young people and adults and pave the way for Wolverhampton College to move from its outdated Paget Road site, which has been identified as land to build much-needed housing.
Its central location will also make it easily accessible for students.
The leader admitted having to rely on ministers for funding brought uncertainty about the project.
He said: "When you need £40m or £50m, money in the bank which the city obviously hasn't, it always worries you that one or others of these bids don't work.
"The council has put in finances, the combined authority is going to put in finances, Stuart Anderson, the MP, is championing it, we just need the Government to recognise we have a problem with Paget Road."