Speaking to the Rezonansi newspaper before the talks, Alasania said: "We are going to the meeting with the president with concrete demands and we will listen to the government's views and concrete offers of what they see as the best way out of this crisis."
Alasania will be joined at the talks with Levan Gachechiladze, a former presidential candidate, Salome Zurabishvili, a former foreign minister, and Kakha Shartava, the leader of the National Forum party.
Despite the month-long protests, which have seen up to 60,000 people take to Tbilisi's streets, Saakashvili has refused to step down until his term ends in 2013.
Clashes at an anti-government protest in Tbilisi and a brief military mutiny outside the capital last week have led to concerns that the unrest could spread through the rest of the country.
The president has insisted that the government's tolerance of the protests are a sign of maturing democracy in the country.
The meeting between Saakashvili and the oppositon comes on the same day as an official opening ceremony for Nato military exercises in Georgia.
The drills have angered Moscow which sees the area as falling within its traditional sphere of influence.
Vladimir Putin, Russia's prime minister, said on Sunday that the army exercises were a tacit sign of Western support for Saakashvili's government.
"Against this background they [Nato] decided to carry out the war games," Putin said in an interview with Japanese media.
"Of course, this cannot be seen as anything other than support for the ruling regime. And why support such a regime?"
Russia has in recent months expressed its opposition to what it calls Nato's expansion into Georgia and Ukraine, two former Soviet republics whose governments have expressed their desire to join the military alliance.