Three people are being tested in Edinburgh and another case is believed to be in Glasgow, Professor Jurgen Haas said.
The head of infection medicine at the University of Edinburgh said he believes there will probably be similar cases in "many other cities" in the UK.
And a patient is being tested to rule out coronavirus at Belfast's Royal Victoria Hospital, it is understood.
None of the patients have been confirmed as having the disease.
They all travelled to Scotland from Wuhan - where the outbreak is thought to have originated - within the past two weeks and are showing symptoms of respiratory trouble, a red flag for the virus.
He said the cases emerged overnight, adding: "The situation will be pretty similar in pretty much all UK cities with a large number of Chinese students.
"It's not too surprising. My suspicion is that there will probably be many more cases in many other cities in the UK.
"None of the cases I know of have been confirmed."
He said there is only one laboratory testing for the virus, operated by Public Health England (PHE).
The professor said the cases have been flagged up through the PHE infection guidelines as they travelled to Wuhan within the last 14 days and are showing signs of respiratory symptoms.
The disease has killed 17 people and infected nearly 600.
Cases have been reported in the US, Japan, South Korea, Thailand, Singapore and Hong Kong.
The Chinese Government has effectively locked down Wuhan, cancelling planes and trains there and in the nearby city of Huanggang.
First Minister Nicola Sturgeon was questioned about the risk to people in Scotland at First Minister's Questions at the Scottish Parliament on Thursday.
She said the situation is being closely monitored, adding: "I should say, that the risk to the public here in Scotland - and indeed the UK - is currently classified as low but that is kept under review."
Health Secretary Matt Hancock said the NHS is "ready to respond appropriately" to any cases of coronavirus that emerge in the UK.
In a statement to the Commons on Thursday, he said while "there is an increased likelihood that cases may arise in this country, we are well prepared and well equipped to deal with them".
Officials from Public Health England have been monitoring direct flights from Wuham city to the UK.
Under measures announced on Wednesday by the UK Government, the planes would have been taken to an isolated area of Terminal 4 at Heathrow after landing.
The Foreign and Commonwealth Office updated its travel advice for China, advising against "all but essential travel" to Wuhan.
Mr Hancock said England's chief medical officer, Professor Chris Whitty, is in contact with international experts and his counterparts to monitor the situation.
He added: "The chief medical officer has revised the risk to the UK population from very low to low and has concluded that while there is an increased likelihood that cases may arise in this country, we are well prepared and well equipped to deal with them.
"The UK is one of the first countries to develop a world-leading test for coronavirus, the NHS is ready to respond appropriately to any cases that emerge, clinicians in both primary and secondary care have already received advice covering initial detection and investigation of possible cases, infection control and diagnostics.
"The public can be assured that the whole of the UK is always well prepared for these type of outbreaks and we will remain vigilant and keep our response under constant review in light of emerging scientific evidence."
Experts from the World Health Organisation (WHO) are due to meet again on Thursday to decide whether to declare a global public health emergency over the virus.