Lazarenko, who served as premier under President Leonid Kuchma from 1996 to 1997, is now in a U.S. prison on charges of corruption, extortion and money laundering. He was arrested in the U.S. in 1999, and was sentenced to nine years in prison and a fine of $10 million in August 2006.
Lazarenko left for the U.S. during the 1999 presidential election campaign in Ukraine, fleeing the charges against him. He sought political asylum there, claiming he had suffered three assassination attempts. Instead, American authorities arrested him.
The former premier spent more than four years in jail waiting for his trial, and was released on a $65 million bail in June 2003. He went back to jail three years later.
Talks on his extradition began on the sidelines of President Viktor Yushchnko's visit to the United States on September 22-25 for the current UN General Assembly session.
A group of Ukrainian security experts will continue the discussions during Yushchenko's next visit to the country on September 29, Ukraine's UNIAN agency said on Thursday.
The agency cited the first deputy secretary of Ukraine's National Security and Defense Council, Stepan Havrysh, as saying that Kiev is very likely to receive a positive reply to its extradition request.