Coleman, chairman of the Senate Permanent Subcommittee on Investigations, could issue the subpoenas as early as Thursday, directly challenging the authority of Paul Volcker (search), head of the Independent Inquiry Committee probing allegations of corruption in the $64 billion U.N.-supervised program.
The subpoenas would be the latest salvo in a continuing fight over diplomatic immunity and access to possibly incriminating testimony.
On Thursday, FOX News also learned that documents that could prove U.N. Secretary-General Kofi Annan (search) lied to Oil-for-Food investigators had been given to Congress Wednesday night.
Last week, Volcker called the chairmen of at least three congressional committees investigating the Oil-for-Food program and told them Congress could not force two former investigators to testify.
Parton and Duncan have accused the panel of downplaying Annan's role in the corruption in an interim report released last March.
In a letter sent to Volcker on Tuesday, Rep. Chris Shays (search), R-Conn., chairman of a House Government Reform subcommittee, warned, "Any resort to reflexive secrecy or legalism undermines the independence and transparency the IIC was meant to bring to the examination" of the U.N. program.
Click here to read the letter.
Shays went on to say that if Parton and Duncan were not permitted to speak to Congress, the panel risked tarnishing its appearance of independence from the United Nations.
"I encourage you to find a way to make the former investigators available to Congress," Shays writes.
IIC spokesman Mike Holtzman issued this response on Wednesday: "We need to keep our eye on the ball and can't be sidetracked by allowing our investigators to be hauled in front of this or any other legislature. The immunities we enjoy are the same as the U.S. Congress. They're there for a reason: to allow us to do our job unimpeded. They are not cloaks and veils."
Last week, a spokesman for Volcker denied he was invoking diplomatic immunity (search) to protect the panel or the United Nations, saying the calls to the committees were made out of "courtesy."
But, the spokesman added, "To subpoena investigators would harm the integrity of the investigation."
Parton's lawyer, Lanny Davis, spoke on his client's behalf.
"Mr. Parton respects the congressional committees and their work," Davis said. "He hopes that Mr. Volcker, the U.N. and the Congress can work this out."
Volcker, the former chairman of the Federal Reserve, was appointed last year by Annan to head up the investigative panel into the Oil-for-Food program.
So far, Volcker's panel has released two interim reports that say the program suffered from mismanagement and raise questions about the role of Annan's son, Kojo Annan (search).
A final report is expected to be released this summer.
After the release of the second report, Parton and Duncan resigned as investigators, objecting to the committee's handling of Annan's dealings with Swiss company Cotecna (search), which was contracted under the program and that once employed Kojo Annan.
"Contrary to recent published reports, I resigned my position as senior investigative counsel for the IIC not because my work was complete but on principle," Parton told The Associated Press in a statement.
Congressional sources told FOX News last week that they believe Volcker is terrified of the damage the investigators' testimony could do to his credibility. U.N. experts said the showdown between Volcker and Congress would be critical.
"It's also being pointed out that if Mr. Volcker is asserting that his team has U.N. diplomatic immunity, then he is admitting that his committee is not in fact independent but a part of the very organization it is supposed to be objectively investigating," said Nile Gardiner of the Heritage Foundation.
Gardiner said it is vital for Parton and Duncan to be heard.
"It's absolutely essential that these two individuals be allowed to testify before Congress to give the full picture. After all, this is a $30 million investigation being funded by the Iraqi people. They demand absolute accountability from this inquiry," Gardiner said.
FOX News' Jonathan Hunt and Per Carlson contributed to this report.