It's been reported the three patients, including a student who has recently arrived in Edinburgh from China, are being tested in the Royal Infirmary.
Meanwhile another individual is undergoing tests in Glasgow for the potentially deadly disease, which has already killed at least 17 people and infected about 600.
Prof Juergen Haas, head of infection medicine at Edinburgh University, told BBC Scotland there were three suspected cases in the Scottish capital.
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Last night China suspended all flights, including international services, out of the city.
It’s thought the virus originated from animals sold as meat, but the rapid spread of the disease - which is similar to the deadly Sars virus - shows it is transmitted between humans.
At least one case has already been detected in the US.
READ MORE: These are the signs, symptoms and causes of coronavirus - and how it spreads
Professor Haas told the PA news agency: "We have currently three cases suspected Wuhan coronavirus in Edinburgh and as far as I understand one case in Glasgow."
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 suspicious 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.
First Minister Nicola Sturgeon has said the Scottish Government is "closely monitoring" a virus which has spread from China.
She was asked at FMQs by SNP MSP Kenneth Gibson about the steps being taken to ensure the safety of Scots after the disease killed 17 people and infected nearly 600.
It is believed the disease, known as coronavirus, emanated from a market in the Chinese city of Wuhan, which has an international airport connecting to 60 destinations across the world.
The First Minister said: "I can assure Kenny Gibson and indeed the chamber that, together with Health Protection Scotland, we are very closely monitoring what is a very rapidly evolving situation.
"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 Protection Scotland are liaising with NHS boards and are currently in daily contact with Public Health England, we're also liaising daily with colleagues in the UK Department of
Health - we're also paying very close attention to the advice and the decisions that come from the World Health Organisation."
She added: "Advanced monitoring measures are being put in place for flights between Wuhan City and Heathrow, that will involve each flight being met by a port health team who will check for coronavirus and provide information to all passengers.
"We're currently considering whether there is any further information that could be provided at Scottish airports.
"This is an evolving situation which we will monitor extremely closely and the Health Secretary and I will make sure that Parliament is updated in the days and weeks to come."
The Chinese Government has effectively "locked down" Wuhan, with planes and trains being cancelled, along with the nearby city of Huanggang.