Both Di Maio and League leader Matteo Salvini have agreed to abandon their own ambitions to lead the government, but crossed vetoes appear to have scotched an array of other candidates.
Five Star, founded as a web-based organization in 2009, will ask its supporters for their opinion on the government program they're negotiating, he said. That person is unlikely to be either Salvini or Di Maio.
The development means Berlusconi could seek a political rebound by pursuing a fourth term as premier when the nation next returns to the ballot box, which could happen in a matter of months if the two parties cannot form government.
Di Maio of the anti-establishment Five Star Movement and Salvini of the anti-immigrant League will hold another meeting on Saturday, this time in Milan, after progress at their previous encounter at the Rome parliament on Friday.
"We're hoping to close the deal as soon..."
The forerunner of Salvini's League, the Northern League, was the main partner in the three center-right governments headed by media mogul Silvio Berlusconi starting in 1994.More news: Dozens dead in clashes as United States opens Jerusalem embassy
"We're not discussing names".
Salvini's League won 17 percent of votes in March, but it was part of a right-wing alliance including Berlusconi's Forza Italia that garnered 37 percent of the vote.
The Corriere Della Sera reported that a Milan court ordered the immediate "rehabilition" of Mr Berlusconi on Saturday, which "cancels all the effects" of his 2013 tax fraud conviction - including a ban on holding elected office.
Both ran for premier in March 4 elections for the Italian parliament.
The opposition Democrats, who controlled the outgoing government, are warning that the League's vow to drastically lower taxes to a flat 15-percent rate, and the 5-Star's promise to give government subsidies to those with low incomes, will spook financial markets and drastically drive up government borrowing costs. "I'm proud that we are discussing, even heatedly, about the kind of Italy we want to create", said Salvini, adding there were differences on issues including immigration, justice reform and infrastructure. They have also pledged to attempt to renegotiate European treaties.