Labor wants more coalition deputies to "air their feelings" about the eligibility of Interior Minister Peter Dutton to be in parliament before trying again to refer him to the High Court.
Mr. Dutton faces questions about his eligibility to sit in parliament because of his family financial interest in two day care centers.
Labor leader Bill Shorten says the opposition will wait until he knows he has the support of some government parliamentarians to try to send Mr. Dutton.
"We have to, of course, wait until there is a majority to refer the matter," he told ABC TV on Sunday.
Julie Bishop this week asked for "clarity" about Mr. Dutton's eligibility and endorsed calls from former Prime Minister Malcolm Turnbull for his recommendation.
Mr. Shorten thinks there might be others like her.
"I should not have to carry the can for the entire Liberal Party, since she had to do it, I think there are other parliamentarians," he said.
"We need to see the government deputies maybe vent their feelings a bit more over the course of the week."
A previous labor motion for a recommendation was rejected by a single vote on August 23.
Section 44 of the Constitution disqualifies any person who has a "direct or indirect pecuniary interest" in any agreement with the Commonwealth.
At the height of the liberal leadership crisis, Attorney General Stephen Donaghue reported that he could not categorically determine Mr. Dutton's status and that only the Supreme Court could do so.
Dutton told parliament on Thursday that the council he has given in relation to his position has "put the issue beyond doubt."
But constitutional law expert Anne Twomey told The Australian on Saturday that the Attorney General's opinion sought information that "significantly increased the risk of disqualification."
Cross representatives Cathy McGowan and Rebekha Sharkie have suggested that they would vote for a reference.