Erdogan made the offer in summit talks with South Korean President Lee Myung-bak held on the sidelines of the G-20 summit meeting in the French city of Cannes, senior presidential press secretary Choe Guem-nak said.
Lee welcomed the request and proposed to hold "substantive negotiations," Choe said.
Last year, South Korea and Turkey held intense negotiations on the US$20 billion project to build four nuclear reactors on Turkey's Black Sea coast. But the negotiations were suspended after the sides failed to work out key differences.
Japan had been expected to win the project. But Turkey's talks with Japan have reportedly been halted since March's nuclear power plant accident in Japan in the wake of an earthquake and tsunami.
South Korea is a global atomic energy leader that relies on nuclear plants for about 40 percent of its electricity needs. The country has also been trying to export nuclear power plants since Korean firms won a massive contract in late 2009 to build four atomic power plants in the United Arab Emirates.
During Friday's meeting, Lee and Erdogan also agreed to make joint efforts to conclude ongoing negotiations on a free trade agreement before the end of the year, Choe said. They also agreed to increase cooperation in the defense industry, he said.
Erdogan asked Lee to visit Turkey next year to mark the 55th anniversary of relations between the two countries, and Lee accepted the invitation, the official said.