Ban is expected to be confirmed as the next U.N. chief next week.
In an interview published by the Financial Times Friday, Ban said current Secretary-General Kofi Annan has made many contributions, but has not been able to visit North Korea during the past 10 years. Ban said he believes he is in a better position to handle the nuclear dispute, because he has a deeper understanding of the inter-Korean relationship.
His published comments come three days after Pyongyang announced it plans to test a nuclear weapon at an unspecified time in the future.
The U.N. Security Council is expected to approve a statement Friday urging North Korea to cancel any planned nuclear weapons test.
North Korea has said testing a weapon is a necessary defensive measure against the United States.
Washington has warned of "international repercussions" if North Korea goes ahead with a nuclear test, but stresses that the warning is not a lethal threat.
Japan's chief Cabinet secretary, Yasuhisa Shiozaki, said Friday Tokyo is stepping up monitoring of North Korea.
Some information for this report was provided by AFP, AP and Reuters.