Labor has written to the government asking if it has legal advice about whether a commercial interest of the assistant health minister, David Gillespie, makes him ineligible to sit in parliament.

The shadow attorney general, Mark Dreyfus, wrote to the attorney general, George Brandis, on 8 February and again on Thursday to ask if the government had advice about whether Gillespie had an “indirect pecuniary interest” in an agreement with the commonwealth, which is prohibited by section 44(v) of the constitution.

According to a Fairfax Media report in February, confirmed at the time by Guardian Australia, Gillespie and his wife own a small suburban shopping complex at Lighthouse Beach in Port Macquarie, New South Wales.

Through their company, Goldenboot, they lease one of the shops to a local woman who runs a newsagent with an Australia Post outlet as a licensee of the government-owned corporation.

Gillespie, a National party MP, insists there is no conflict of interest or constitutional breach because his company has no agreement or deal with Australia Post.

The constitutional law expert George Williams said there was arguably a case that the arrangements constituted an indirect pecuniary interest but it depended on the outcome of the high court case about former senator Bob Day’s eligibility to be elected.

On Wednesday the high court ruled the former Family First senator had been ineligible, expanding the definition of an “indirect pecuniary interest in any agreement with the public service of the commonwealth”, banned by section 44(v).

In his letter Dreyfus noted that Day was disqualified because he had an “indirect financial interest in a commercial property that was leased to the Department of Finance to serve as his taxpayer-funded electorate office”.

“There is a clear correlation between Mr Day’s situation and that of the Coalition member for Lyne, the Hon Dr David Gillespie MP, who owns a retail premises which is occupied by an outlet of Australia Post.”

Dreyfus said the Day high court decision “renewed these serious concerns about Dr Gillespie”, and asked Brandis if he had sought advice from the solicitor general about his eligibility.

He said the government had a responsibility to have Gillespie’s constitutional eligibility independently tested because the risk he might be disqualified was a “very grave matter” that could affect the composition of the House of Representatives.

The constitutional law expert Anne Twomey told Guardian Australia the high court had broadened the ban so that it not only captured members and senators over whom the executive government could potentially exercise influence but also parliamentarians who sought “to benefit their private interests above their public duty”.

“It is also broader because it is not confined to legal or equitable interests in an agreement,” Twomey said.

“There is, however, no relevant interest if the agreement in question is one ordinarily made between the government and a citizen.”

Twomey said if Gillespie “had an arms-length commercial arrangement with the lessee, who in turn had an ordinary commercial arrangement with Australia Post, where there was no conceivable influence applied or conflict between private interest and public duty, it is probably OK”.

“Nonetheless, I suspect that many MPs will be (or ought to be) rushing off to check that their financial interests comply.”

On Thursday, Fairfax Media reported that the government could recover salaries and allowances from Day and Rodney Culleton, who was elected a Western Australian senator for One Nation then ruled ineligible from the time of his election.

A spokeswoman for the special minister of state, Scott Ryan, said the Department of the Senate was responsible for “recovery of debts arising from overpayment of salary”, suggesting Day and Culleton might owe debts for receiving salaries and allowances for the period they sat in the Senate while not eligible.

Day’s period of ineligibility stretched from 26 February 2016 until his resignation in November.

“The special minister of state can only consider waiving a senator or member’s debt if the individual concerned or the Department of the Senate makes an application to do so,” the spokeswoman said.

Guardian Australia has contacted Gillespie for comment.