Former prime minister Tony Abbott has hit out at one of his most loyal supporters, Liberal senator Cory Bernardi amid talk the South Australian is preparing to form a breakaway conservative party movement, predicting it would be wildly successful but harm the Coalition.

Writing in his favoured News Corp newspaper The Australian, Mr Abbott warns Senator Bernardi against leaving, saying MPs should remember they are only in the Parliament because of the party and it's their duty to "try and fix it and not to leave it" if they identify problems.

But Mr Abbott predicts that if Senator Bernardi does split he could win 10 per cent of the vote and have senators elected under the conservative banner in every state.

"My guess is that a new entity called the Conservative Party could win up to 10 per cent of the total vote here in Australia but almost all of it would be at the ­expense of the Liberal-National Coalition," Mr Abbott writes.