The two forces sat down to talk on Thursday morning after League ally Silvio Berlusconi essentially gave them the green light by stepping aside on Wednesday night, relinquishing his claim to any cabinet seats for his conservative Forza Italia party.
While Berlusconi may no longer be an obstacle for a new government, Italian president Sergio Mattarella has announced that he will require certain guarantees in order to give the anti-establishment parties his approval.
The anti-corruption Five Stars, which came in second at 32.5 percent, offered to form a government with the League on condition it ditches scandal-tainted Berlusconi, who has been convicted of tax fraud and is a defendant in various trials concerning alleged orgies at his home while he was still prime minister of Italy. But given Mattarella's refusal to give Salvini the mandate, Berlusconi said he wouldn't stand in the way of the League taking responsibility to try to form a government with the 5-Stars.
Berlusconi, leader of the Forza Italia party, said in a statement that he would not veto such an administration, and would support measures in line with the policies of the center-right alliance led by the League. "We should go to the polls in July".
Mattarella has given the parties 24 hours to reach an agreement.
"We are doing everything possible to form a political government and thereby respect the will of the Italians, but if this isn't possible there can be no neutral government", Giorgetti said.More news: Dwane Casey Voted COY by Coaches Association
Until now the sticking point had been Silvio Berlusconi, the former prime minister whose Forza Italia party is a junior partner in a right-wing alliance led by the League. He said his party would "loyally support" laws in line with the center-right's program.
But Mr Diebel said that by the former Prime Minister clearing the way for this, it does not yet mean the end of his political career and could prove a good move if Five Star Movement and Lega fail to work together successfully.
"A political government is now more probable, and a mild negative market reaction is likely tomorrow", said Vincenzo Longo, an analyst at IG Markets.
The Italian election result earlier this year saw massive gains for anti-establishment parties but as in Germany, a potential coalition deal has taken months.
Luigi Di Maio, head of M5S said on "No confidence in a "neutral" government, which is synonymous with technical government".
An alliance between Five Star and the League has always been considered the most destabilising outcome of the election because both parties have attacked European Union fiscal rules, banking regulations, trade deals and sanctions against Russian Federation. That would trigger a snap election perhaps for July.