Koizumi told senior ruling party lawmaker Taku Yamasaki during a meeting late Wednesday that he was considering a trip as Prime Minister Shinzo Abe's special envoy, according to the report.
Koizumi wants to urge the North to abide by the 2002 Pyongyang Declaration, a bilateral pact in which the North promised to maintain peace and stability in Northeast Asia and freeze its missile program, the report said.
The mass-circulation daily, Yomiuri Shimbun, carried a similar report.
"Denuclearizing the Korean Peninsula is a responsibility I want to take on as politician," Koizumi was quoted as saying by Yomiuri.
The reports did not say when Koizumi's visit might be.