"The Five Star Movement and the League have informed the president that they are in talks to try to come to a possible government accord and that they need 24 hours to develop this initiative," a statement from the presidential palace said.
Crucially, former Italian premier Berlusconi later on Wednesday signalled he would not block a possible coalition deal between the two parties.
According to Italian media, League leader Matteo Salvini's main political allies had been exerting strong pressure on Mr Berlusconi to give his approval to a Five Star-League government, while the Italian tycoon's own Forza Italia (FI) party remains deeply divided on the issue.
"If another political force of the right-wing coalition wants to take on the responsibility of forming a government with the Five Star Movement we will take note of this choice with respect," Mr Berlusconi said in a statement.
Mr Berlusconi said the M5S did "not have the political maturity to assume this responsibility" but that an agreement between it and the League would not mark the end of the "alliance" between FI and the League, especially in the regions they led together.
Italy has been locked in a political impasse since the March 4 election failed to produce a clear winner.
A right-wing coalition led by the nationalist League won the most seats at the polls while the M5S led by Luigi Di Maio became the biggest single party, but neither obtained enough seats for a majority.
To form a coalition they have to agree on a prime minister and a common program.
"We are going to sit down at the table and begin to talk about the issues for the country. Then we will talk about names," Mr Di Maio told the Italian press.
For his part Mr Salvini said in a statement that "we still have to work on the program, on dates, on the team and the things need doing... either we reach a conclusion, or we return to the voters".
After three failed rounds of consultations thus far, Italy has looked to be heading either for a caretaker government, chosen by the president, or fresh elections as early as July.
It had been widely expected that President Sergio Mattarella would nominate his pick for prime minister to lead a "neutral" government on Wednesday.
However, both the League and M5S are staunchly opposed to a caretaker government and without their support the initiative would not pass a confidence vote in parliament.
Mr Mattarella's response to the extension request was not immediately clear, although it is thought he would be unlikely to refuse.
For the past two months the two parties have been scrambling to reach an accord for a coalition government but have repeatedly hit a wall over the League's coalition partner Mr Berlusconi - who is himself barred from office.
M5S leader Luigi Di Maio had insisted that the League ditch Mr Berlusconi and FI as a prerequisite to forming a government together, something League leader Salvini refused.
The regional governor of Italy's northern Liguria region, Giovanni Toti, who holds a lot of clout within FI, had suggested earlier Wednesday that his party could exercise a "benevolent abstention" in the face of a coalition.