The Creative City project hopes to create 100,000 jobs in the region and add Â£8bn to the local economy.
The new galleries would be part of the new Curzon Square Museum Quarter.
Launching the scheme, Culture Secretary Ed Vaisey urged West Midlands business leaders to invest in creative industries.
The three new galleries would be Ikon 2, built on Curzon Street as a sister gallery to the current Ikon.
A museum of contemporary art will be launched with works from leading modern artists.
And the Curzon Street railway station buildings could house a museum of photography.
Martin Mullaney, cabinet member for leisure, sport and culture at Birmingham City Council, said the building earmarked for the photography museum was currently empty and needed a new use.
He said: "We have probably one of the largest photographic collections in Britain, showing photographs throughout the whole history of Birmingham and it's there in cardboard boxes."
The museum of contemporary art would house works by artists such as Francis Bacon, Henry Moore and David Hockney.
A feasibility study is currently being carried out and will reveal the expected cost of the three museums.
Mr Mullaney said the council was in the process of bidding for a collection of national importance which would bring tourists to the city.
He added the new galleries could be paid for by money from the private sector, the Heritage Lottery Fund, the Arts Council and the government.
"We want to show that we have got a vision for Birmingham and an ambition to put Birmingham on the international stage so that we are up there with the likes of Barcelona and Berlin," he said.
Three art galleries could be created in Birmingham as part of an ambitious scheme to attract investment in the arts.