World Health Organisation officials are in talks about building up a stockpile of drugs for poorer countries to fight a possible bird flu pandemic.
Almost 60 people have died after contracting bird flu
Tamiflu, made by Swiss firm Roche, works by reducing the symptoms and the risk of a carrier passing on the virus.
WHO director general Jong-wook Lee said he hoped even more could be stockpiled in the future.
Many developed countries, including Britain, have already said they will stockpile the antiviral drug.
The UK government has warned that, without measures to contain an outbreak, 50,000 people in the UK could die.
So far, 57 people have died from the H5N1 strain of avian flu, but no mutation with a human flu has been seen.
However, health experts around the world fear it will, and are working to develop vaccines which could be used to protect people in the event of a pandemic.
Stockpiling antiviral drugs is another way of trying to reduce the impact.
The WHO is currently in talks with Roche about ordering more of the drug.
It already has a small stockpile that would be used by health professionals in the event of an outbreak.
Speaking in Thailand, one of the countries which has been hardest hit by bird flu, Jong-wook Lee said rigorous health monitoring in countries at risk was essential in containing outbreaks.
"The really important issue is surveillance, surveillance, surveillance.
"On the map there are lots of boundaries, but the virus does not carry a passport."
He added that he was expecting to have "What I am expecting to have is initially one million, and I hope that that can be multiplied."
Last week, Roche said it was considering donating a "substantial amount" of Tamiflu to the WHO.