Mr Kurz quit as Austrian Chancellor last month amid pressure over a corruption scandal.
It has now been reported he will also step down from his role as leader of the People’s Party (ÖVP).
Interior Minister Karl Nehammer is likely to take over as ÖVP leader.
Mr Kurz is reportedly stepped down as his “enthusiasm” was “lost” due to the corruption allegations.
He also reportedly wants to spend more time with his newborn son.
Mr Kurz and nine others were under investigation following raids at locations linked to the ÖVP.
He denies allegations he used government money to ensure favourable polls in a newspaper.
Mr Kurz said last month: “What’s required now is stability.
“To resolve the impasse I want to step aside to prevent chaos.
He said he would continue to be leader of his party and sit in parliament as he fought the charges against him.
Mr Kurz said: “First and foremost, however, I will of course use the opportunity to disprove the allegations against me.”
Mr Kurz became leader of the ÖVP in May 2017.
He led the party to victory in Austria’s elections later that year.
The corruption allegations relate to the period between 2016 and 2018.
Finance ministry funds are alleged to have been used to ensure favourable polls in a newspaper.
MORE TO FOLLOW