The former minister said the move would have a "transformative" impact on the city and show the Government's commitment to its levelling up agenda.
Wolverhampton is understood to be one of seven potential locations for a second chamber touted by Levelling Up Secretary Michael Gove, who wants peers to decant from Westminster for the duration of the works.
South Staffordshire MP Sir Gavin said Wolverhampton would be the "ideal" spot for the Lords to move to.
"It now seems likely that while these extensive restoration works take place the Lords will need to move out of Westminster," he said.
"Wolverhampton, with its central location and a large number of sites close to the railway station that are ripe for development, really would be ideal. It is an extremely sensible and viable option.
"Such a move would undoubtedly be transformative. It would change the face of the city and give an enormous economic boost to the entire region, bringing with it an investment of hundreds of millions of pounds.
"It would also be very much in line with the Government's levelling up agenda. How wonderful it would be to see the Queen's Speech delivered from Wolverhampton."
Mr Williamson has written to Lord McFall, the Lord Speaker, requesting a meeting to discuss a potential relocation to Wolverhampton.
He said while a permanent move "would not be out of the question", even a decant would have a "significant impact" as it be would likely last for several years.
The move would require a main chamber for hundreds of peers as well as numerous other sites such as committee rooms and offices.
Lord Austin, the former Dudley North MP, has long been an advocate of moving parts of government out of London.
He said: "If there's a case for moving both the Commons and the Lords out of London – and I think there is – then why not move them to other parts of Britain?
"Why does it have to be in London? The city doesn't work, congestion is a nightmare and property prices are ridiculous.
"I think it's about time we had some really radical ideas about taking pressure off London and supporting growth and jobs and investment in the rest of the country."
No start date has been set for the start of the work to the House of Lords, which is expected to cost up to £13 billion, providing the 'cheaper option' of a full decant takes place.
Earlier this year a report said the restoration could take up to 76 years if politicians and peers were not moved.
Mr Gove, who has an office at Wolverhampton's i9 development where the Department for Levelling Up, Housing and Communities has its regional headquarters, has reportedly rejected the peer-favoured move to the Queen Elizabeth II Centre in Westminster.
He has led calls for a move out of the capital, recently telling the Commons he would "wholeheartedly welcome the relocation of the House of Lords to one of our great cities".
He said Stoke-on-Trent would be an "excellent home" for peers, and is also understood to have listed Burnley, Sunderland and Plymouth among other potential options.