The question of how to fill the long-vacant South Australian Senate seat left empty by Bob Day could be answered within days as the High Court hands down its decision.

Senate President Stephen Parry told parliament on Thursday the Court of Disputed Returns would hand down its decision on Wednesday at 10.15am.

The seat has been vacant since last year after the Family First senator resigned to deal with his collapsing building business, but there are questions about whether he was validly elected in the first place, and how the vacancy should be filled.

Mr Day's eligibility is being challenged on the grounds he may have directly or indirectly benefited from the commonwealth through a lease arrangement relating to his Adelaide electoral office.

Under section 44 of the constitution, a member or senator can be disqualified where there is "any direct or indirect pecuniary interest in any agreement with the public service of the commonwealth".

Former Labor senator Anne McEwen, who lost her seat at the July federal election, is a party to the case, given it could open the door for her return to parliament if he is disqualified.