The city has reportedly emerged as the frontrunner to host the new second chamber, while Birmingham is also said to be in the running.
Tory chairman James Cleverly confirmed that plans to move the Lords outside of London were being considered, but did not say which locations were under discussion.
According to the Sunday Times, disused government-owned land close to York railway station has already been identified as a possible site.
When asked about reported proposals, Mr Cleverly, speaking to Sophy Ride on Sunday on Sky, confirmed that there were a number of options on the table.
Looks like the Tories have been following the Labour leadership contest. But instead of just moving the existing House of Lords up north, they should scrap it entirely in favour of a democratically elected Senate, as I’ve argued. All lawmakers should be accountable to the people. pic.twitter.com/lWPTAvXt7H— Rebecca Long-Bailey (@RLong_Bailey)January 18, 2020
“What we are looking at is a whole range of options about making sure every part of the UK feels properly connected from politics," he said.
“When the PM stood up the day after the election and said this is going to be the people’s government he meant it. That meant connecting people with government and politics.
“The referendum in 2016 wasn’t just about our relationship with the EU, it was about millions of people and their relationship with politics as a whole.”
When pressed to say if the move would happen, he replied: “We might. It’s one of a range of things that we are looking into.
"But fundamentally what this is about is about demonstrating that we are going to do things differently.”
Challenged again, he said: "It’s one of a range of things we’re looking at. Trust me - we’re going to be radical.”
Rebecca Long-Bailey, who is vying to become Labour leader, has previously said she wants to replace the House of Lords with an elected senate, based outside of London, if she succeeds Jeremy Corbyn.
She tweeted this morning: "Looks like the Tories have been following the Labour leadership contest. But instead of just moving the existing House of Lords up north, they should scrap it entirely in favour of a democratically elected Senate, as I’ve argued. All lawmakers should be accountable to the people."
The restoration of the Palace of Westminster already requires some 800 peers to another building for six years from 2025