The Tory South Staffordshire MP says he has reached out to Labour Wolverhampton Council leader Ian Brookfield over launching a bid for the competition, which is run every four years by the Department of Digital, Culture, Media and Sport (DCMS).
Mr Williamson, the Education Secretary, said the city would make an ideal candidate "due to its rich history and cultural diversity".
Coventry won the last contest and is the current City of Culture, following previous winners Derry-Londonderry and Kingston upon Hull.
Mr Williamson said: "Making Wolverhampton the UK's next City of Culture would bring well-deserved recognition to the city.
"This would not just benefit this dynamic and culturally diverse city but would also bring visibility, benefits, and opportunities to the West Midlands, including my own constituency of South Staffordshire.”
The city plays host to the Wolverhampton Art Gallery, home to one of the country’s largest pop art collections.
It also has the Grand Theatre, which dates from 1894; the Lighthouse Cinema; the Grade II-listed Wolverhampton Central Library; Bantock House; Wightwick Manor and St Peter’s Collegiate Church.
The city has a rich musical history, with Slade, Cornershop, Babylon Zoo, Beverley Knight and Liam Payne all hailing from the area.
Launching the 2025 competition, Culture Secretary Oliver Dowden, said: "UK City of Culture is a fantastic showcase of the huge impact culture has in towns and cities across the country.
"From Derry-Londonderry, to Hull and Coventry, previous winners have shown how the competition can deliver greater cultural participation, drive economic regeneration and boost local pride.
"I encourage towns and cities across the UK to put forward bids for 2025 and champion their local arts and culture scene.
"I’m also delighted to confirm the competition will run in future years, as a sign of our commitment to levelling up culture across the whole of the UK."
A number of cities have already been put forward for the 2025 title, including Bradford, Chelmsford and Southampton.
The county of Cornwall has also made a bid, as has Lancashire.