The World Health Organisation (WHO) was expected to make the decision on Wednesday, but said they needed more information before deciding what to do, describing it as an "evolving and complex situation".
More than 440 cases of coronavirus have been confirmed in China's Hubei province, of which Wuhan is the capital, and officials said at least 17 people have died there.
Following a meeting of an emergency committee on Wednesday, WHO director-general Tedros Adhanom Ghebreysus said: "There was an excellent discussion during the committee today, but it was also clear that, to proceed, we need more information.
"For that reason, I have decided to ask the emergency committee to meet again tomorrow to continue their discussion and the chair, Dr Houssin, has agreed with that request.
"The decision about whether or not to declare a public health emergency of international concern is one I take extremely seriously, and one I am only prepared to make with appropriate consideration of all the evidence."
He said there is a team in China working with local experts and officials to investigate the outbreak, and he added: "We will have much more to say tomorrow."
Planes to be isolated at Heathrow
Earlier on Wednesday, the Department of Health and Social Care (DHSC) said precautionary measures were being put in place at Heathrow after cases of the virus spread to other parts of the world.
There are three direct flights a week from Wuhan in China to Heathrow Airport, landing at around 6pm on Monday, Wednesday and Friday.
Under the new measures, it was planned that planes would be taken to an isolated area of terminal four.
The captain of each flight would then tell passengers during landing to let a flight attendant know if they feel unwell, and these details would then be passed on to public health teams at the airport who would carry out further checks.
Meanwhile, the Foreign and Commonwealth Office updated its travel advice for China, with a spokesman saying: "In light of the latest medical information, including reports of some person-to-person transmission, and the Chinese authorities' own advice, we are now advising against all but essential travel to Wuhan.
"The safety and security of British nationals is always our primary concern and we advise British nationals travelling to China to remain vigilant and check our travel advice on gov.uk."
Public Health England (PHE) upgraded the risk to the UK population from coronavirus from "very low" to "low".
Public transport suspended
The Associated Press reported the state-owned People's Daily newspaper said in a tweet no-one would be allowed to leave Wuhan starting at 10am and that train stations and the airport will shut down.
The newspaper is also reported to have said that Wuhan authorities are saying city buses, subways, ferries and long-distance shuttle buses would also be temporarily closed.
A handful of cases have been identified abroad, including in Japan and the US, but there have been no reported cases in the UK.
Professor Neil Ferguson, director of the Medical Research Centre for Global Infectious Disease Analysis, said the estimated number of people infected with coronavirus in Wuhan is around 4,000, with a range between 1,000 and 9,700.
Health system not 100% foolproof
Asked whether it was possible the virus had already reached the UK, professor Ferguson said he could not rule it out.
He said: "We can't rule out that possibility.
"Border screening, and in this case, in the UK, alerting the health system is not 100% foolproof - there could be a mild case.
"The UK is not a major destination of visitors travelling out of Wuhan around the world though.
"So I would say it was unlikely, but can't be completely sure."
Explaining why there is global concern about the virus, Dr Josie Golding, epidemics lead at Wellcome, said it was because so little is known about it.
She added that there was a lot of "missing information", like how easily it can be transmitted and where it is coming from.