The junior Coalition partner's cabinet representation is at risk of falling from five to four people, unless Mr Turnbull intervenes.

At the same time, positioning is already underway for the deputy leadership post vacated by Ms Nash, with a possible four-cornered contest in the offing.

The four MPs most often mentioned for the role of deputy leader of the Nationals are cabinet ministers Matt Canavan and Darren Chester, outer-ministry member Michael McCormack, and assistant minister Keith Pitt.

Ms Nash will most likely be replaced by Liberal candidate Hollie Hughes, who was the next person listed on the joint Liberal-National Senate ticket in NSW in 2016.

However, Ms Hughes could be found to be ineligible because of her recent appointment to the Administrative Appeals Tribunal. If that eventuates, fellow Liberal candidate, former Major General Jim Molan, could take the post.

Assuming Barnaby Joyce wins the December 2 byelection in his northern NSW seat of New England and a Liberal takes Ms Nash's place in the Senate, there will be 84 Liberal-aligned MPs in the Parliament, up from 83 MPs; and 21 Nationals MPs, down from 22.

This small change in the ratio would be enough to ensure the Nationals are only entitled to four cabinet spots, while the Liberals could gain a number – under the formula used by the Coalition parties – in a Turnbull cabinet of 20, 21 or 22 people.

Currently there are just three Nationals – Mr Chester, Senator Canavan and acting leader Nigel Scullion – in the 20-member cabinet, with the fourth spot being held open so that if Mr Joyce wins back his seat he will go straight back into cabinet.

Fairfax Media spoke to several Nationals MPs on Tuesday who conceded that, in line with the complicated formula that governs how many Liberals and Nationals make up the cabinet, the junior partner's representation is set to fall.

"Under the Coalition agreement it is done on a proportional basis, and our proportion will fall as a percentage so our ministerial spots will be under review," the MP, who asked not to be named, said.

"We may well lose a cabinet spot but we could also pick up an outer ministry and lose an assistant ministry."

That assessment was supported by several other Nationals MPs.

But another Nationals source said Mr Turnbull may take into account more than just the ratios dictated by the Coalition agreement and – as an act of good faith – put a fifth Nationals MP in the cabinet to ensure good relations with the junior Coalition partner.

"Malcolm wouldn't risk the relationship," that source said. "This won't just be about the maths."

In the short term, however, all agreed the party's current focus was on helping Mr Joyce win back his seat of New England in the looming byelection.

Further complicating the picture, if either Mr McCormack or Mr Pitt were to win the deputy leader position, they would automatically be entitled to a cabinet spot – which would mean Mr Turnbull would have to promote a fifth Nationals MP to cabinet – or sack one of Mr Canavan, Mr Chester, or Mr Scullion.

This is unlikely to happen.

All of these calculations are taking place against the backdrop of what is expected to be a broader reshuffle by the end of the political year.

The announcement by Senate president Stephen Parry late on Tuesday that he, too, may be a dual citizen and could have to step aside could further complicate the cabinet arithmetic.

However, former Liberal senator Richard Colbeck would be the frontrunner to take Mr Parry's spot.