Mr Barak will also be called the "senior deputy to the prime minister", giving him greater status than all other deputies appointed in the new cabinet.
"This country deserves stability within the government," Mr Vilnai said. "If we go to elections, ongoing work in government ministries will be suspended and we will lose critical time and resources."
On Wednesday, Kadima representatives met United Torah Judaism members to discuss the possibility that the Charedi party will join the new government.
Ms Livni has also offered places in the new government to the Pensioners party and the left-wing Meretz party. If Ms Livni fails to form a new coalition soon, Israel will go to general elections which Likud leader Binyamin Netanyahu is predicted to win.
Mr Vilnai predicted that once Labour joins the government, the strictly Orthodox Shas Party, currently a member of the government, will also join Ms Livni's new government.
Shas is demanding that Jerusalem be taken off the negotiating table with the Palestinians, and is calling for an increase in child allowances for families with numerous children. Aware of Shas's importance, Mr Netanyahu visited the party's spiritual leader, Rabbi Ovadia Yosef, and asked that Shas refrain from joining Ms Livni's new government.
Mr Netanyahu assured the rabbi that if he won a general election he would offer Shas a senior position in the government.
