A challenger has unexpectedly stepped forward to take Nick Xenophon's South Australian Senate seat, Premier Jay Weatherill has told State Parliament.

The casual vacancy for Mr Xenophon's seat was expected to be filled by his handpicked candidate, Rex Patrick.

But Mr Weatherill said the Nick Xenophon Team's fourth-placed candidate at the last election, Tim Storer, had stepped forward to take the seat.

He said the Government would seek legal advice from the Crown Solicitor's Office on how to proceed and fill the seat.

"I can … confirm that I have received a letter marked private and confidential from lawyers representing Mr Timothy Storer, a Senate candidate for the NXT Party at the 2016 federal election," Mr Weatherill said.

Ordinarily, a senator who voluntarily quits Federal Parliament would have a successor chosen by their party, and rubber-stamped by State Parliament.

Had Mr Xenophon lost his recent High Court case over his citizenship, Mr Storer may have been his replacement based on a recount, rather than the party's choice of Mr Patrick.

Mr Xenophon said he was shocked and disappointed at the actions of Mr Storer.

"The changes to Section 15 of the Australian Constitution in the late 1970s were all about ensuing that it was a nominee of the party that filled a casual Senate vacancy," Mr Xenophon said.

"It would absolutely fly in the face of the spirit and intent of those amendments for the SA parliament to choose anyone other than the party's nominee, Rex Patrick."

Senate one short while Parliament deliberates

In the meantime the party has asked that the letters from Mr Storer's solicitor be made publicly available.

Mr Weatherill said there would be a joint sitting of Parliament on November 14 to consider a replacement senator.

This means there will be at least two days when the Senate is one down because Mr Xenophon has already quit.

Mr Xenophon formally resigned from the Senate on Tuesday and also announced the Nick Xenophon Team would be renamed SA Best (Federal).

He is running in the electorate of Hartley at next year's South Australian election.

Mr Xenophon said he was particularly surprised by Mr Storer's actions as he had expressed a strong wish to run as a SA Best candidate in the upcoming state election.