The bank believes about $17.5 billion will be needed for 2004 and roughly $37.5 billion for the years between 2005 and 2007, the Japanese Nihon Keizai Shimbun financial daily reported on Wednesday.
The paper added that the World Bank, along with the International Monetary Fund (IMF), had informed Japan and other nations of the figures.
World Bank President, James Wolfensohn, said last week that the bank would not make any estimates public until it had finished consulting on the issue with Iraq representatives by early October.
But he added that United States reconstruction estimates between $50 billion and $75 billion were "in the ballpark".
The Nihon Keizai said the World Bank would officially present the estimates at a donors' meeting to be held in Madrid on 23-24 October.
In Washington, a US Senate committee on Tuesday passed a $87 billion bill for Iraq’s reconstruction.
Republicans on the Senate Appropriations Committee muscled the bill through after defeating Democrats' attempts to make Iraq repay some of the bill's $20 billion for its reconstruction, to trim $10 billion from the package and to limit Bush's discretion over its spending.
"If we are sceptical ... it's because the administration has coiled out the rope and hung itself with its own rhetoric"
Senator (Democrat), Illinois
The committee unanimously voted out the bill, but Democrats said that did not mean they would back the final measure.
Republicans had guaranteed Democrats a lengthy debate on the bill, abandoning plans to pass it by this weekend. Instead, Senate Majority Leader Bill Frist of Tennessee said the goal was to pass it by 17 October, after a recess next week.
The committee's bitter exchanges and party line votes on amendments portend a rough debate. Democrats charge that the $20 billion for Iraq's rebuilding comes at the expense of domestic needs and should not be borne by US taxpayers alone.
Democrats also said that before the war the White House assured lawmakers that Iraq would finance its own reconstruction.
"If we are sceptical ... it's because the administration has coiled out the rope and hung itself with its own rhetoric," said Senator Richard Durbin, an Illinois Democrat.
Testifying on the Iraq package before the House Appropriations defence subcommittee, Defence Secretary, Donald Rumsfeld, said US companies should be favoured in contracts under the $20 billion for reconstruction.
"On the money that the US taxpayers are paying for Iraq, we certainly ought to be focusing to the extent we can on American contractors and suppliers," Rumsfeld said.