Labor backbencher Graham Perrett wrote to the Australian Federal Police in December asking them to investigate Mr Brough and others singled out in a Federal Court judgment that dismissed former staffer James Ashby's sexual harassment case against Mr Slipper.
Justice Steven Rares described that case as an abuse of process, saying Mr Ashby had acted in combination with fellow Slipper staffer Karen Doane and Mr Brough, a former Howard government minister who is now running for Mr Slipper's seat of Fisher.
In his letter, Mr Perrett said the judgment indicated there may have been a "political conspiracy" designed to harm Mr Slipper and the federal Labor government.
"This conspiracy involved using a fabricated sexual harassment claim to politically damage and publicly humiliate Mr Slipper," Mr Perrett wrote at the time.
AFP Commander Errol Raiser responded to Mr Perrett's letter this month, saying the agency's investigation had been suspended until after Mr Ashby's appeal, due in court on May 30.
"As the facts surrounding the appeal are consistent with your referral, the AFP has suspended its evaluation of the matter until the outcome of the appeal has been finalised," Cmdr Raiser says.
Mr Perrett says he is disappointed by the AFP's decision.
Mr Slipper queried why the federal police investigation has been suspended, given Mr Brough is not involved in the application to appeal the court decision.
"To my knowledge, (Mr) Brough and (former staffer Karen) Doane ... are not seeking to contest the judge's adverse findings against them and thus have not sought leave of the court to challenge His Honour's findings," Mr Slipper said in a statement to AAP on Thursday.
"In these circumstances it is difficult to understand why the AFP has suspended/postponed (though not cancelled) its investigation of the matters raised in Mr Perrett's letter to the AFP commissioner."
Mr Slipper said he would be surprised if the Liberal National Party continued to keep Mr Brough as the party's candidate for Fisher.
He said it was clear that the AFP was taking Mr Perrett's complaint "very seriously".
"This must be a concern for the LNP or at least those members of the LNP who still want (Mr Brough) to be their candidate," Mr Slipper said.