Chancellor Christian Stocker announced this week that he supports a constitutional ban.
He said he does not want Austria’s children and grandchildren to grow up in an Islamic state.
Stocker says political Islam, meaning Islam interpreted as a political system, clashes with Austrian democracy and Western values.
His People’s Party had earlier voted down a similar proposal from the far-right FPÖ, then reversed course in late August.
Integration Minister Claudia Bauer is now drafting the proposal for the coalition partners.
The liberal NEOS and the Social Democrats (SPÖ) have both said they are ready to vote in favour.
Stocker insists that freedom of religious belief and practice will stay protected.
A constitutional law needs a two-thirds majority in parliament, and when asked how he would get one, the chancellor said he did not know.
There is no draft text and no vote date yet.
Critics argue the term is vague and could end up hurting ordinary Muslims, pointing to Austria’s earlier headscarf ban in schools.
Supporters say the state must stop extremist networks, like the Muslim Brotherhood, before they take root.
Austria’s government-backed research center has already examined groups linked to political Islam.
