Jacob Rees-Mogg is believed to have suggested the House of Commons sit in one of the Scottish, Welsh or Northern Irish parliaments for a fortnight every year.
This would see MPs gather in Holyrood the Senedd or Stormont every September, with the location changing each year.
The Commons Leader is believed to have discussed the idea with the Speaker Lindsay Hoyle, who is reportedly yet to be convinced.
Despite concerns over costs and too many MPs, a source suggested it would “bring Parliament closer to the people”.
A UK Government spokesperson said: "Any decision on the location of the UK Parliament is for the UK Parliament."
The discussion follows plans in Westminster to move towards policy making with a wider UK focus.
However, the idea has now been dismissed by the SNP's shadow Leader of the House Pete Wishart MP.
He said: "Not content with taking away powers and funding from the Scottish Parliament, Rees-Mogg and the Westminster Tories are now setting their sights on taking over the building itself – even though MSPs will be sitting.
"The idea is not only utterly laughable, but it demonstrates just how out of touch the Tories are. Their arrogance when it comes to Scotland literally knows no bounds.
“It's clear that the only way to properly protect our Parliament and powers is to become an independent country.
"The upcoming election is the most important election in Scotland’s history and it comes down to a stark choice – who should decide the country’s future, the people of Scotland or Boris Johnson's Tories?
"With both votes SNP we can put Scotland’s future in Scotland’s hands, not Boris Johnson’s."
SNP depute leader Keith Brown said: "Having already taken powers and funding from the Scottish Parliament, the Tories have confirmed that they now want to take over the Parliament building as well, despite the fact MSPs will be sitting there – nothing could better illustrate Tory arrogance and ignorance of Scotland.”
A Scottish Parliament spokesperson said: “We’ve not been approached by the Leader of the House.”