The report obtained by The Associated Press also accused the company, Cotecna Inspection S.A., and Annan's son, Kojo, of trying to conceal their relationship after the contract was in place.
The conclusion from the report, scheduled to be released later Tuesday, was not the clear vindication that the secretary-general had wanted, though the investigation led by former U.S. Federal Reserve Chairman Paul Volcker did not accuse the U.N. chief of corruption.
The report said "there is no evidence" that the selection of Cotecna for an inspection contract under the oil-for-food program "was subject to any affirmative or improper influence of the secretary-general in the bidding or selection process."
Weighing all the evidence in the 144-page report and the credibility of the witnesses, the investigators said "the evidence is not reasonably sufficient" that Annan knew about Cotecna's bid in 1998.
The report found that Kojo Annan was not forthcoming with either his father or the committee and accused him of consistently trying to hide the nature of his relationship with Cotecna.
It said there were still "significant questions" about Kojo Annan's business dealings with respect to the program, and said an investigation was continuing.
"Although the new Volcker report stops short of accusing the Secretary General of financial gains in the scandal, it makes damaging accusations about Kofi Annan's failure to prevent his own son from being involved in corruption and conflicts of interest," said CBS News Foreign Affairs Analyst Pamela Falk from the U.N. on Tuesday.
"Stacked up with the recent admission by Kofi Annan that he met on several occasions with officials from Cotecna -- the Swiss company involved in the scandal -- and that incriminating documents were destroyed by Annan's staff, the report is yet another blow to U.N. credibility," Falk said.
In a letter annexed to the report, Kojo Annan's lawyer, William R. Taylor, rejected any claim that Kojo Annan had not been wholly cooperative with the committee. But Taylor admitted he had not told his father the entire truth.
"Mr. Annan has consistently acknowledged that he was not completely candid with his father when the Cotecna-U.N. contract first attracted publicity in late January 1999," Taylor wrote. "He regrets the embarrassment that omission caused to his father and to the United Nations and accepts responsibility for it."
The report is the second issued by the team of investigators led by Volcker. It comes a week after Annan called for the biggest overhaul of the United Nations in its 60-year history. It also coincides with allegations of sex abuse by U.N. peacekeepers and of sexual harassment and mismanagement by senior U.N. staff.