Dr David Nabarro, who heads the UN drive to contain the virus, told weekly Portuguese newspaper Expresso that "only two mutations are needed for it to become easily transmissible among humans".
"I wake up every morning thinking that today could be the day that I will see a report about a strange case of bird flu among humans," he said in the interview published on Saturday.
Dr Nabarro's statement came amid reports that the virulent H5N1 bird flu virus had reached Italy and Greece.
The virus was found in swans in three Italian regions: Puglia and Calabria in southern Italy, and Sicily.
In Greece, the H5N1 strain was found in three swans in the north of the country.
In Nigeria, authorities were investigating whether the bird flu virus had spread to humans after several people were reported ill, the health minister said on Saturday.
"I wake up every morning thinking that today could be the day that I will see a report about a strange case of bird flu among humans"
Dr David Nabarro,
UN bird flu panel chief
Eyitayo Lambo, the health minister, said his officials were investigating "one or two cases of reported illnesses" among humans which could be due to bird flu, though none had been confirmed so far.
The H5N1 bird flu virus has killed tens of millions of birds since 2003, and there have been at least 165 confirmed cases of the strain spreading to humans, causing about 90 deaths, mostly in Asia.
The virus has spread from Asia to eastern Europe, and this week Nigeria reported Africa's first known outbreak of the deadly strain of the disease.
Experts have long said that the H5N1 virus could mutate into a form that is easily transmitted by humans and spark a global pandemic, potentially killing millions.
Nabarro said he had told governments around the world to prepare for the arrival of a human-to-human strain of the virus "as if this will happen tomorrow".
In 1918, an influenza pandemic that was believed to have originated in birds killed more than 40 million people around the world.
Subsequent pandemics in 1957 and 1968 had lower death rates but still caused widespread disruption.