Liberal senator Cory Bernardi appears to be on the verge of leaving the Liberal party and starting a political party called Australian Majority, which already has its own website.

The new political group and website - www.am.org.au - has been set up by Senator Bernardi for release in the new year, The Australian reports.

Internet source code shows the new website is linked to the outspoken politician's existing Australian Conservative website, according to the newspaper.

"The name Australian Majority was also registered as a trademark by a company controlled by Senator Bernardi's wife late last year," the paper said.

It appears Cory Bernardi may be leaving the Liberal party. (AAP)

Former prime minister Tony Abbott wrote to Liberals yesterday, telling them a split would doom the party amid fears of a conservative splinter.

The Australian reports him as saying: "The first duty of the leader is to keep the party together".

Former speaker Bronwyn Bishop does not think Senator Bernardi will split from the party, but said Prime Minister Malcolm Turnbull has work to do to take the party back to the centre-right.

"The leadership of the Liberal Party can be a broad church, but not broad enough to have socialist philosophy creeping into it," she told Sky News.