| However, many other La Nina events have not seen novel flu strains spread around the world, they caution. [bbc]
So while the climatic phenomenon may make a pandemic more likely, they say, it is not sufficient on its own - and may not be necessary either.
La Nina is the cold cousin of El Nino - the two collectively making up the El Nino Southern Oscillation (ENSO).
"Certainly ENSO affects weather and precipitation and humidity around the world," said Jeffrey Shaman from Columbia University in New York.
"But the effects are very varied around the world - there's no coherent picture."
Nevertheless, the last four pandemics - the Spanish Flu that began in 1918, the Asian Flu of 1957, the Hong Kong Flu of 1958 and the swine flu of 2009 - were all preceded by periods of La Nina conditions.
What pandemics have in common is that they all feature novel strains of the virus to which people have not developed immunity.
Typically these are created when two existing strains infecting an animal such as a bird or a pig exchange genetic material.
Satellite thermal image La Nina conditions emerge as a tongue of cold water (purple) in the eastern Pacific
The link to La Nina events is not clear. But recent research has shown that some wild birds' patterns of flights and stopovers during migrations, or moulting times, differ between El Nino and La Nina years.
"Our best guess is this brings together birds [in La Nina conditions] that don't otherwise mix, and that allows the genetic reassortment to take place," Professor Shaman told BBC News.
Yet the fact that many other La Nina periods have not been followed by a pandemic indicate that other factors must also be involved.
If the swine flu pandemic of 2009-10 was part of this pattern, the crossing of viral strains must have had something to do with birds as well as pigs.
As wild migratory birds will sometimes visit farms and as domestic flocks of ducks or chickens often live alongside pigs, especially in developing countries, this is quite feasible.
Professor Shaman cautions that the link is far from being firm enough that it could be used as a tool to forecast pandemics.
But the monitoring of birds, pigs, people and the genetics of the influenza virus have all been stepped up in response to recent outbreaks of both swine flu and bird flu.
And this, he believes, should in time show whether the theory is correct.
"Now we can look at viral gene flow in a number of birds, pigs and people - and we might be able to get something more statistically robust, to get a better sense of the mechanisms."