The two met in 2000 when Kim Dae-jung was still president and both said they wanted to meet again.
The diplomacy comes at a time when North Korea is further isolated by claims by the United States that it is a rogue nation and part of President Bush's axis of evil.
The 82-year-old Kim Dae-jung said he won't get into details about the proposed meeting until North Korean leader Kim Jong-il responds to his request for a visit, the Korea Times reports.
Kim Dae-jung said he will surely go though, weather and health permitting.
He chose train travel to spur the opening of a cross country train line overdue to begin service.