The High Court will this morning rule on whether former South Australian senator Bob Day was validly elected to Parliament at last July's federal poll, and how his Upper House crossbench seat should be filled.

The Senate has been operating without Family First's vote since Mr Day resigned last October, and the Coalition could find itself courting his replacement to support its legislation.

Mr Day resigned from the Senate after his construction business Home Australia Group went into liquidation last October.

But the decision today will kickstart the process to replace him.

If the Court finds Mr Day's election was valid, it falls to the Family First party to pick his successor — which would then be formalised by a joint ceremonial sitting of the South Australian state Parliament.

Mr Day's preferred replacement is his former chief of staff, Rikki Lambert, who is now employed in the same role by newly independent South Australian senator Cory Bernardi.

SA state Upper House member Robert Brokenshire is also expected to throw his hat in the ring.

But if the court rules his election was invalid, it will likely force a recount of the SA Senate vote.

With Mr Day's name excluded from any recount, "above the line" preferences for Family First would likely flow to Kenyan-born Lucy Gichuhi, who was second on the party ticket.

But if there is a decision that the whole Family First ticket is invalid, then all of the votes from that party would go elsewhere.

It is that outcome former Labor senator Anne McEwan is hoping will be adopted, increasing her chances of returning to the Senate after her defeat last July.

With the defection of fellow SA senator Cory Bernardi to the crossbench, the Coalition only has 29 votes in the Senate.

It needs 39 votes to pass legislation, which means the Government needs to convince 10 crossbench senators to support its agenda in the event Labor and the Greens block any bills.

Bob Day's former electoral office in Kent Town, Adelaide. ( ABC News, file photo )

Last year the Federal Government asked the Senate to refer Mr Day's election to the High Court after concerns about the leasing arrangement for his electorate office in the suburb of Kent Town in Adelaide's inner east.

The Constitution prevents an individual from sitting in Parliament if they have a direct or indirect financial interest in any agreement with the Commonwealth.

Documents before the court show that when Mr Day was told by the Senate he could not lease an office in a building he owned, he transferred the property to Fullerton Investments, which was to be run by a family friend, Debra Smith.

Although no rent was ever paid by the Commonwealth, the arrangement was that money would go to an account named Fullerton Nominees, which was controlled by Mr Day.

At a hearing in Melbourne in January, Mrs Smith said she had agreed to take on the building after a request from her husband John, but had had no involvement after that.

Ms McEwan had hoped to use the hearing to broaden the scope of the High Court case, and strengthen her bid for a recount which would favour her re-election.

Justice Michelle Gordon found the evidence from the Smiths about the transfer fell short of Ms McEwan's claims there was an arrangement where Mr Day would maintain control.

But she noted that it would be for the full court to decide if the arrangement was legally effective, and removed Mr Day from any effective benefit.