Sunderland has been suggested as one of several locations for the House of Lords to relocate to while Parliament undergoes refurbishment.
Michael Gove, who is Levelling Up Secretary, is said to have written to Lord McFall of Alcluith suggesting locations including Stoke-on-Trent, Burnley and Sunderland.
In the letter, reported in the Sunday Times, Mr Gove said he knows "cities and towns across the United Kingdom would be pleased to extend their hospitality to peers".
He is quoted as saying that having "carefully reviewed the proposed arrangements", he "will not support the use of the QEII Centre as an alternative location".
The Queen Elizabeth II Centre conference and exhibition space is just a few minutes' walk from the Palace of Westminster in London.
In the letter, which the Sunday Times said was also sent to Prime Minister Boris Johnson and Cabinet Secretary Simon Case, Mr Gove suggested a move elsewhere in England, Scotland or Wales.
He is reported to have written: "As the minister responsible for levelling up, it is clear to me that the House of Lords moving elsewhere, even for a temporary period, would be widely welcomed.
"I have carefully reviewed the proposed arrangements and...I will not support the use of the QEII Centre as an alternative location.
"I propose to establish dedicated liaison points for you in my department to support you in identifying a suitable location for the House of Lords in the North, Midlands, South West, Scotland or Wales. I would, of course, be happy to meet you to discuss this."
Boris Johnson had previously suggested a move to York, but in 2020 the body responsible for parliament's restoration said it would not be considered because it raised "constitutional implications".
A spokesperson for the Department for Levelling Up, Housing and Communities declined to comment.
Earlier this year, a report showed that restoring the Palace of Westminster without finding a new home for MPs could take up to 76 years, with a repairs bill reaching £22 billion.
The project's sponsor body and delivery authority said the cheapest option would involve a "full decant" of the palace for between 12 and 20 years, with the work costing in the region of £7 billion to £13 billion.
In this scenario, with MPs elsewhere for much of the time, the report estimated the restoration would take between 19 and 28 years.
A House of Lords spokesperson said: "The Lord Speaker has just received this letter from the Secretary of State. We will respond to it in due course.
"In March the House of Lords and House of Commons Commissions reaffirmed their united commitment to preserve the Palace of Westminster for future generations.
"Both Commissions will meet in June to consider future arrangements for the restoration and renewal programme and proposals will then be put to both Houses of Parliament. This process will set the way ahead.
"Any decision about whether and where to relocate the House of Lords, whether on a permanent or temporary basis, is ultimately a matter for the House itself."