The populist Five-Star Movement and the far-right League party are debating their respective conceptions of Italy - not premiers - in their talks on forming a government, League leader Matteo Salvini said on Monday.
"We are not discussing names of possible prime ministers although I know that the topic fascinates journalists," he said.
"We are just discussing - indeed heatedly - our ideas of the Italy we want," Salvini said.
He made the remarks after a meeting on Monday with Italy's president Sergio Mattarella.
After a meeting earlier on Monday with Mattarella, Di Maio said he had asked the head of state for "several more days" of talks on a tie-up with the League.
Di Maio leads Italy's largest parliamentary party after the inconclusive 4 March election while Salvini heads the centre-right alliance - the biggest political bloc.