Di Maio said that the nominee would be a politician and "not a technocrat" after meeting Salvini in Milan on Sunday.
Lega leader Matteo Salvini and M5S leader Luigi Di Maio have both discussed the matter with President Sergio Mattarella, saying they were close to securing a deal on naming next prime minister. According to Italian media reports, the nominee will be a "third party" belonging to neither the League or the M5S and would have worldwide authority.
Di Maio and Salvini will meet in Rome on Monday before updating the president.
If Mattarella endorses the candidate, programme and cabinet lineup then he could nominate a prime minister on Monday, paving the way for a government to be sworn in this week before facing a vote of confidence in both houses of parliament.
The two parties announced last Wednesday they were looking to forge a government more than nine weeks after an inconclusive election, but despite making progress on policy priorities they have yet to decide who should lead the coalition.
The leader of the country's anti-establishment Five Star Movement says he has reached an accord with the right-wing League.
The parties have reportedly agreed on rolling back increases to the age of retirement while Five Star is broadly willing to follow the League's hardline anti-immigration policies.
Five Star has also called for a universal basic income scheme for the unemployed, while the League supports a flat income tax.