The claims against Mr Slipper, made in court documents obtained by The Daily Telegraph, allege he recruited 33-year-old James Ashby only to pursue a sexual relationship with him.
In an application filed to the Federal Court, Mr Slipper allegedly made unwelcome advances toward Mr Ashby and sent him explicit text messages making his sexual intentions clear.
In one case, Mr Slipper reportedly asked Mr Ashby to shower with the door open at his Canberra home.
In several text messages to Mr Ashby, he signed off using an "X", indicating a kiss, while in others he allegedly used gay slang and quizzed his adviser's sex life.
The newspaper also reports the Australian Federal Police have been asked to investigate whether Mr Slipper, 62, misused Cabcharges, a taxpayer-funded perk.
Among the allegations is that Mr Slipper signed several Cabcharge vouchers that were later filled out by a limousine driver.
Mr Ashby is seeking a court order that Mr Slipper undergo counselling and training in anti-discrimination, as well as compensation from the federal government and the Speaker.
Mr Slipper, who is overseas on a parliamentary delegation that included a stop in Hungary, has denied the claims, the newspaper reports.
