Outspoken Liberal senator Cory Bernardi has created a new political group called 'Australian Majority', in a move likely to fuel speculation he will split from his party.

The Weekend Australian reports the website 'am.org.au', which is linked to his existing Australian Conservative web page, and a logo are set to be launched in the new year.

It is not yet known whether Senator Bernardi plans to launch the re-branded movement as a a political party or a right-wing alternative to the GetUp group.

Former prime minister Tony Abbott and Tasmanian senator Eric Abetz are reportedly among MPs urging Senator Bernardi not to split from the Liberal Party.

Conservative figures including Queensland MP George Christensen and Senator Abetz have also called on Prime Minister Malcolm Turnbull to address a perceived shift away from the Liberal Party's base.