The news comes after former Prime Minister Silvio Berlusconi annouced he will not prevent a new coalition government, with anti-establishment Five Star Movement and right-wing Lega parties reportedly close to agreeing a ruling coalition for the country following weeks of back-and-forth negotiations.
The League-Forza Italia coalition won the most votes in a March national election at roughly 37 percent.
President Sergio Mattarella announced Monday that there are only two options to find a new government: either political parties accept a caretaker government until December and elections take place afterwards; or Italy heads to a new vote in July or in the fall.
Giancarlo Giorgetti, a politician with the League for more than 20 years who has been mooted as a potential prime minister, was also at the meeting, as was Vincenzo Spadafora, a deputy with M5S.
In a joint statement after meeting on Thursday, Mr Di Maio and Mr Salvini described a "positive climate to define the government's agenda and priorities" and said "technical" meetings among staff would begin in the afternoon.
Two months after Italy's inconclusive general elections, the populist Five Star Movement (M5S) and conservative Northern League are nearing an agreement for a governing majority. The anti-establishment group had refused to negotiate with the centre right as a whole, saying it was only willing to form an executive with the League.
A basic income and a flat tax are "important starting points" for the government programme, M5S MP Alfonso Bonafede said after the first government-contract talks between the two parties. "Either we reach a conclusion, or we return to the voters".
President Sergio Mattarella, a key player in Italian politics, is eager to avoid an immediate election, fearing it will result in another stalemate and damage the economy.
"Today, to ask Forza Italia to give external support (to a government) seems a very bad move which we an only say no to", said Maria Stella Gelmini, Forza Italia leader in the lower house of parliament. "We spoke about it and there's no problem", he said.
The 81-year-old Berlusconi, who had previously opposed a Five Star-League tie-up, said he would respect a decision of "another political force of the center-right to create a government with Five Star". "There are no details yet on the individual measures: in these days we will work to prepare the initial proposals and then we'll get into the details". Meanwhile the possibility of a "staffetta" or "baton change" between the League and the M5S for the premiership was aired.