Di Maio added that he and Salvini would meet with Italian President Sergio Mattarella on the issue of the new government later on Monday.
Mr Mattarella summoned Mr Di Maio and League leader Matteo Salvini for an update more than 10 weeks after an inconclusive parliamentary election.
Italian economist Giulio Sapelli said that he had been addressed by the right-wing League party, and the anti-establishment Five Star Movement (M5S) about the possibility of heading the government they are now seeking to form after the March 4 parliamentary election.
The parties have also agreed on tightening laws on illegal immigration across the Mediterranean and want to push the European Union on changing the "Dublin regulation", by which refugees must seek asylum in the first European Union state they reach.
Following a weekend of intense negotiations, the leader of the anti-establishment M5S Luigi Di Maio and Salvini had been widely expected to announce a "government agreement" and a nominee for prime minister on Monday afternoon.
On its own, the League picked up 17%, while the M5S is by far Italy's largest single party after conquering almost 33% of the electorate. Last Wednesday, Berlusconi said he wouldn't prevent the parties from forming a government. They are the two largest groups in parliament and together can muster a majority in both houses.
Officials from both parties say privately that candidates are being sought, and that Di Maio and Salvini have agreed that neither of them will be premier.
But the biggest single bloc is a centre-right alliance of Mr Salvini's League and Mr Berlusconi's Forza Italia party that garnered 37% of the vote.
Even so, it is still unclear how all this will square with Italy's commitments to reduce its budget deficit and its public debt, which at more than 130 per cent of gross domestic product (GDP), is the highest in the eurozone after Greece.
Just who would lead a populist government has yet to be decided.
Italy's populist parties asked for more time to form a government on Monday as they thrashed out a wild spending spree that would cost the country more than €100 billion (£88 billion) and set it on a collision course with the EU.
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