Sauli Niinisto and Sanna Marin said in a joint statement they expected a decision in the next few days.
The move comes amid a surge in public support for Nato membership following Russia's invasion of Ukraine.
Moscow said Finland's move was a threat to Russia and the further expansion of Nato would make Europe less stable and secure.
Previously, Russia has threatened unspecified measures - and on this occasion too, Kremlin spokesman Dmitry Peskov did not say exactly how Russia would respond.
"Everything will depend on how this expansion process plays out, the extent to which military infrastructure moves closer to our borders," he said.
Finland shares a 1,300-km (810-mile) border with Russia. Until now, it has stayed out of Nato to avoid antagonising its eastern neighbour.
Finland will formally announce its decision on Sunday after it has been considered by parliament and other senior political figures.
Sweden has said it will announce a similar decision on the same day.
Nato Secretary General Jens Stoltenberg has said he expects the process of giving Sweden and Finland membership to happen "quite quickly".
President Niinisto and Prime Minister Marin said in their statement they had wanted to give the Finnish public space to discuss the issue but that time for a decision was approaching.
"Nato membership would strengthen Finland's security," it said. "As a member of Nato, Finland would strengthen the entire defence alliance. Finland must apply for Nato membership without delay."
Speaking to journalists later, Mr Niinisto responded to Russian concerns and blamed the move on Moscow's invasion.
"Joining Nato would not be against anyone. You caused this. Look in the mirror," he said.
An opinion poll last week put support in Finland for joining Nato at 76%, with 12% against, a big swing towards membership since before the invasion.
Finland and the USSR were on opposing sides in World War Two, with the Finns famously fending off a Soviet invasion in 1939-40.
But Finland lost 10% of its territory in the final peace agreement and remained non-aligned throughout the Cold War.
Its accession to Nato would more than double the length of Russia's borders with the alliance. Sweden does not have a border with Russia.
News ID : 654