According to The Sun, the MSP for Edinburgh Central reportedly told friends she would make the move as a stepping stone for a Tory leadership bid and abandon Scottish politics to take a peerage instead.
It is thought Ms Davidson, who is due to give birth to her first child in November, could move to London as early as next year after her maternity leave.
However, the party have denied the rumours and insisted she wants to be First Minister of Scotland.
A friend of the Scottish Tory leader told the newspaper: “Ruth told me that she is having a rethink about the next few years.
“It’s dawning on her that she needs to prove she can run something bigger than just the Scottish Tory party to show members she would be good leader of the party and the country.
“You can renounce peerages these days, so that’s how she’d do it as a stop gap before fighting a Westminster seat at the next general election, whenever it comes.”
A spokesman for Ms Davidson did not deny conversations about any future in Westminster however they also said she has not decided to quit the Scottish Parliament before 2021.
A spokesman for the Scottish Tories said: “This simply isn’t the case.
“Ruth wants to be First Minister of Scotland.”
Senior Conservative friends said she needs to prove herself by running one of the big Offices of State and improve her chances of leading the British party.
The popular Scottish Conservative boss has always denied speculations she will move into British politics.
She became leader of the party in Scotland in 2011 and is an MSP for Edinburgh Central.