The transfer of money has been managed by Ri Chol, who stepped down in April as the communist country's ambassador to Switzerland, said Open Radio for North Korea, which specialises in North Korean news.
Ri has been considered one of Kim's closest aides and looks after his secret funds abroad, it said. The US-based Radio Free Asia carried a similar report about the transfer of money.
Analysts say Kim's personal funds have been dwindling because of economic difficulties and tightened international sanctions on the reclusive communist state.
There have been widespread reports that Kim Jong-Un, 27, is being groomed to take over from his 68-year-old father, who suffered a stroke in August 2008.
Some analysts say the North is likely to designate Kim Jong-Un as the leader's political heir when it convenes a rare meeting of key communist party delegates in September.
South Korea's spy chief Won Sei-Hoon said last month that Kim Jong-Il's poor health was driving him to speed up preparations to transfer power to his son, who has been taking a greater role in policy-making.