The High Court, sitting as the Court of Disputed Returns, will take the rare step of hearing from three witnesses today before it considers whether former Family First senator for South Australia Bob Day was validly elected.

The Senate referred the case to the High Court last year, but today's hearing has been prompted by former Labor senator for South Australia Anne McEwen, who lost her seat at the 2016 election.

The case is focused on who owned a building in Kent Town, South Australia, where Mr Day set up his electorate office, and whether the lease arrangement breached the constitution.

The core of the case is the allegation that Mr Day, who has since resigned from the Senate, may have breached section 44 (v) of the constitution by having a direct or indirect pecuniary interest in the building which housed his electorate office.

Mr Day denies claims he held an interest in the lease, saying he did once own the building but sold it to a company called Fullarton Investments in 2014.

If the allegation is upheld that would render his declaration to run for the Senate invalid, and could impact who is chosen as his replacement.

If the court finds Mr Day was elected validly, he will likely be replaced by another Family First candidate.

However if his election is deemed invalid, a countback will likely be held to determine his replacement.

Witnesses to be questioned on lease arrangement

Ms McEwen wants to call evidence from witnesses with knowledge of the arrangements made when the building was sold, including the woman who was the sole shareholder and director of Fullarton Investments.

The building in Kent Town, Adelaide at the centre of a High Court dispute involving former senator Bob Day. ( ABC News )

Her lawyers will also be raising questions about the declaration made by Mr Day when he nominated for the Senate, and whether his high profile drew more votes to Family First than the party would have won if he had not stood.

The parameters of the case between Mr Day and the Commonwealth have been in place for some time, but today's hearing is necessary because of a series of disputes between Mr Day and Ms McEwen over the facts of the case.

High Court Justice Michelle Gordon will have to rule on whether evidence given by the witnesses should be part of the case, which will go before the full court next month.

It is a high stakes game for Ms McEwen, who is waiting not just to hear whether Mr Day was validly elected or not, but also what orders the court will make about how the vacancy should be filled.

The Court of Disputed Returns is yet to rule on another challenge to the election of former One Nation senator Rodney Culleton.

However, the Senate has already taken steps to replace him after he was declared bankrupt by the Federal Court.