The report of the investigators scrutinising the oil-for-food programme is set to be formally released on Tuesday.
An official said the report has found that the UN secretary-general did not pay enough attention to the apparent conflict of interest involving his son, Kojo.
Kojo worked for Cotecna Inspection SA at a time the Swiss firm won a UN contract to certify the import of goods under the oil-for-food programme, the official said.
The Independent Inquiry Committee, headed by former US Federal Reserve chairman Paul Volcker, has also criticised the secretary-general for failing to detect shortcomings in the UN's internal bureaucracy that allowed problems in the oil-for-food programme to continue until 2003, the official said in New York on Monday, speaking on condition of anonymity.
Kojo Annan worked for Cotecna in West Africa from 1995 to December 1997 and then as a consultant until the end of 1998 - when the oil-for-food contract was awarded.
The UN oil-for-food programme is
now a subject of intense scrutiny
He remained on the Cotecna payroll until 2004 on a contract to prevent him from working for a competitor in Nigeria or Ghana.
Oil-for-food investigators have been seeking to verify the Swiss firm's claims that it paid Kojo Annan about $365,000 over eight years.
The secretary-general, his son, and Cotecna all deny any link between Kojo Annan's employment and the awarding of the UN contract to the company.
UN spokesman Fred Eckhard has said there will be no UN comment until the report is formally released.