Conservative Party chairman James Cleverly said the idea was an option being considered by ministers.
Mr Cleverly told Sky News: "What we are looking at is a whole range of options about making sure every part of the UK feels properly connected from politics."
The MP for Braintree 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, Mr Cleverly said: "We might.
"It’s one of a range of things that we are looking into."
He added: "But fundamentally what this is about is about demonstrating that we are going to do things differently."
In December the Prime Minister was criticised following the appointment of former MP Nicky Morgan to the Lords in order that she remain in the Cabinet.
Former Conservative MP Zac Goldsmith, who lost his seat in the 2019 General Election, was also made a life peer.
International Development Secretary Alok Sharma welcomed the idea of relocating the Lords.
Speaking to the BBC he said: "I’m not involved in the detail of it, but actually as a principle, as a principle it’s a perfectly good thing that we are connecting government to all parts of the country.
"I mean, my own department, we’ve got over 1,000 people based in Scotland, East Kilbride.
"We’re investing in that.
"And I think it’s absolutely right that if you want to be a government of the people, you must reach out to people across the country."