Some of the Americans who were held captive say he was, but Iran emphatically denies it. The White House is taking the allegations "very seriously" – as well it might. For if it is established that Mr Ahmadinejad did play a major role in an episode still seared on America's collective memory, this could scuttle all efforts to improve bilateral ties between Washington and Tehran, and deal a blow to talks to curb Iran's nuclear programme.
The incoming Iranian president has already indicated he favours an uncompromising line in the talks in which the EU powers are seeking a halt to uranium enrichment activities, vital to its suspected quest for a nuclear weapon.
The evidence on the crucial question is mixed. Back when the US embassy was seized on 4 November 1979 – in retaliation for the Carter administration's refusal to hand over the exiled Shah – Mr Ahmadinejad would have been 23, about the average age of the student hostage-takers.
A picture circulating on the internet shows a dark-haired and bearded young man leading a blindfolded hostage in the compound, but whether it depicts a youthful Mr Ahmadinejad is a matter of hot dispute.
For some of the US hostages, there is no doubt. "This is the guy; there's no question about it," Chuck Scott a retired US army colonel told the Associated Press. "You could make him a blond and shave his whiskers, put him in a zoot suit and I'd still spot him."
He was a "hard-ass", Mr Scott added separately. "Some of the guards told me he was very strict, and very anti-American."
Other hostages too said they were convinced that Mr Ahmadinejad was one of their captors. "He was not a very nice fellow; he called us pigs and dogs," a retired Navy captain, Donald Sharer, told ABC's Good Morning America. David Roeder went further, telling AP: "He was present at my personal interrogation."
William Daugherty, who worked for the CIA in Iran, said a man he is convinced was Mr Ahmadinejad was in a group escorting a Vatican representative early in the crisis. "It's impossible to forget a guy like that," Mr Daugherty said, "the way he acted, the fact he gave orders, that he was older. Certainly he was one of the ringleaders."
But some of the Americans who underwent the ordeal of 444 days in captivity are less certain, saying they could not remember Mr Ahmadinejad being there, although they admitted that he did look "somewhat familiar".
The denials from Iran were adamant – a reflection perhaps of an awareness that confirmation would make normalisation of relations with Washington and the West even more problematic. Mr Ahmadinejad's office has flatly denied the reports. Mohsen Mirdamadi, a top student leader at the time, told the BBC Mr Ahmadinejad had "never been with them even for one minute". Abbas Abdi and Hamid Jalaiepour, two other students who played a big role, said the same.
The three are reformists who oppose the hard-line policies of Mr Ahmadinejad, and would have no reason to hide his involvement now. Others say that the figure in the photograph appears taller, and does not resemble pictures of him as a young man on the president-elect's website.
But the denials have done nothing to re-assure the Bush administration. The White House spokesman said the statements from former hostages "raise many questions" about the man about to lead the government of a country classified by George Bush as a founder member of the "axis of evil". The US was trying to establish the truth about the questions, which it was taking "very seriously".
Speculation that Mr Ahmadinejad might have been among the hostage-takers began earlier this week when John Simpson, the BBC's world affairs editor, wrote that he instantly recognised Mr Ahmadinejad from his role in the siege.
444-day ordeal that shook America
Militant students stormed the US embassy on 4 November 1979, taking 63 American diplomats and staff hostage in what was to become a 444-day siege that shook the confidence of the US and cost Jimmy Carter a second term as president.
Iran was still in the thrall of the Islamic Revolution, which ousted the unpopular dictator Shah Reza Pahlavi, when the students, supported by the Revolutionary Guard and the Ayatollah Khomeini, demanded he be extradited from the US to face trial. Hostage-takers said the action was meant to be a show of strength against US intervention and that events spiralled out of control.
After two weeks 13 female and black hostages were released. A rescue mission failed dramatically when a sandstorm brought down US helicopters, killing eight.
It was not until Ronald Reagan's inauguration on 21 January 1981 that the remaining 52 hostages were freed after Iranian assets were released. Three of the four Britons had to wait a further month before being released, and the last, Andrew Pyke, was not freed until February 1982.
In Iran the anniversary of the storming is still celebrated as a "national day of fighting against global arrogance".