"The government wants Lithuania to remain a country with nuclear energy, but we do not have the financial means to build the new reactor," Brazauskas told journalists.
"It would cost some 2 billion euros, a fantastic price for us, so we should work on this issue and seek advice," Brazauskas said after a government meeting on nuclear energy issues.
The prime minister said Lithuania would seek advice from European Union (EU) energy companies and international experts further afield.
"If they show some interest, then we could consider building a new reactor," Brazauskas said.
Lithuania halted the first of two reactors at Ignalina on December 31 in line with a pledge to the EU made during membership talks. The Baltic state acceded to the EU in May last year.
The deal provides for the complete closure of the facility in 2009.
The Ignalina plant, which supplied more than 70 percent of all energy consumed in the Baltic state, operated two RBMK reactors - the same type as those used at Ukraine's Chernobyl nuclear plant, which exploded in 1986 in the world's worst civil nuclear disaster.
The EU has promised to finance the closure of the Ignalina plant, estimated at between two and three billion euros (2.5-3.75 billion dollars) over 30 years. More than 200 million euros have already been allocated to prepare decomissioning the first unit.