Home Affairs Minister Peter Dutton has threatened to turn the tables on the Labor opposition if it keeps pursuing him over the au pair scandal, saying he "kept a list" of MPs who asked him for help on immigration cases and he is "gathering information" to expose Labor's hypocrisy.

Meanwhile, Labor and the Greens have announced they will increase the pressure on Mr Dutton with a no confidence motion when Parliament returns next week, which will test the government's control of the House of Representatives.

They will also use a Senate inquiry this week to probe the au pair controversy. Mr Dutton on Monday insisted he had "nothing at all to hide" and challenged Labor to interrogate him in the chamber.

"Labor can ask me 10 questions every day when we go back if that’s what they want to do, but they’ll get a whack back," he said.