Australia's first Kenyan-born senator could be booted from the Parliament just months after she was recruited by the Liberals.

Lucy Gichuhi defected from Family First to the Liberal Party in February, making the shock announcement alongside Prime Minister Malcolm Turnbull, who described her as an "inspiration" and a "true Australian success story".

But the ABC has been told the party's right-faction has never embraced Senator Gichuhi — a social conservative — and is moving to install Adelaide City Councillor Alex Antic above her on the party's Senate ticket.

That would push Senator Gichuhi to the fourth position, which is considered unwinnable.

One source told the ABC that if Mr Antic is on the ticket, the former Family First senator would be "consigned to the dustbin".

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But another source noted Senator Gichuhi's traditional family values would appeal to sections of the party, and said she had the support of the Liberal State President John Olsen, who "invested a lot luring her into the [party]".

Her loss could spark controversy given the dearth of women — and lack of diversity — in Coalition ranks, an issue that is once again in the spotlight following LNP MP Jane Prentice's surprise preselection defeat in Queensland.

At this stage, Assistant Minister Anne Ruston is expected to take the top spot on South Australian ticket, given her seniority, with Mr Antic and fellow conservative Senator David Fawcett battling it out for the second and third positions.

Senator Fawcett was elected to the Senate in 2010 and is considered a more traditional conservative.

Cabinet Minister Simon Birmingham — who is from the moderate faction — described Senators Ruston, Fawcett and Gichuhi as "outstanding" and had a message for preselectors in his home-state.

"I hope and expect that all three will be pre-selected again," he said.

"They have my full support, I'm sure they'll have the full support of the team."

Senator Ruston said she was confident preselectors would make the right decision.

"Lucy is an inspiration, anyone who saw her maiden speech and knows Lucy's story knows she is an inspirational person," she said.

"She also brings a great deal of diversity to our Parliament."

While the Liberals are hopeful of winning three Senate seats at the next election, sources say it is more likely they will end up with two, which could also spell trouble for Senator Fawcett.

But the party's immediate focus is contesting the looming by-election in Mayo, having just endorsed Melbourne-based lawyer Georgina Downer as its candidate.

The Liberals are "vaguely hopeful" of winning that by-election, one of three the party is contesting in the wake of last week's citizenship-related resignations.