On March 31, China announced that the virus was discovered in humans for the first time. There were 21 confirmed deaths and 104 confirmed cases by Monday.
The fear is that the virus will mutate and become transmissible between humans, triggering a pandemic.
But for now, there seems to be no evidence of human-to-human transmission.
Keiji Fukuda, assistant director general for health security and environment at WHO, said they have spent the last three days meeting government officials in Shanghai and visiting the agricultural market.
Officials acknowledged that certain "family clusters" exist, where members of one family become infected, but they are saying this is not related to human-to-human transmission.
Fukuda said it is "not clear why we have these small clusters."
He said there are certain families where more than one person contracted the flu and likely caught it from animals.
"With other avian influenza viruses we have seen where you can have limited, person-to-person transmission, so there's always the possibility," he said.
The difference between "sustained" transmission and "limited" transmission is that limited transmission happens between family members or medical personnel caring for the ill, but no one else.
Many cases in Shanghai are the limited type, including a man who contracted the virus from his father and a man whose wife had the flu.
"Family clusters in general do not change our understanding of the characteristics of the disease," Feng Zijan said.
"It is still passed from poultry to people and there is no evidence of human-to-human."