If Mr Pacitti, 24, is confirmed as having swine flu, that would represent the first case of onward transmission of the virus in the country.
Ms Sturgeon said: "Obviously the circumstances around this individual do give us cause for concern - the symptoms don't give us cause for concern, but the circumstances give us cause for concern."
Later Ms Sturgeon will meet business, council and trade union leaders as well as members of the emergency services to update them on the situation.
A virologist at the National Institute for Medical Research, Dr John Macauley, told BBC Radio Scotland the results would be important in showing how strong the virus is.
He said: "If the people who import the virus into the country infect other people and they go and infect more then I think we are in a pandemic situation.
You try to stay calm but at the back of your mind there is the possibility that you might die
Iain Askham
"But at the moment, if for example this is one case only in which we see onward transmission in the UK and that's reproduced elsewhere, maybe this virus isn't fit enough to cause a pandemic but just a big epidemic."
However, Dr Alan McNally, senior lecturer and influenza diagnostics researcher at Nottingham Trent University, downplayed the significance of onward transmission.
"We know that [the flu] is transmitted from human to human, it has happened in other parts of the world and we know it will happen here.
"I know that there will be interest in it because members of the public will see that they don't need to have been to Mexico to get it."
Tests are continuing as amid efforts to contain the spread of the virus
Graeme Pacitti works at Falkirk Royal Infirmary, and is understood to play in the same six-a-side football team as Iain Askham, who with his wife Dawn became the UK's first confirmed cases.
A neighbour of Mr Pacitti, who also works at the infirmary, said she was concerned by a lack of information provided.
"I'm waiting to hear whether or not I'm to go into work," she said.
"No-one has told us anything, I have a five week old grandson and I've had to tell my family to keep away."
Meanwhile the Askhams have spoken of how they feared they might die from the virus.
Iain told the Daily Mail: "You try to stay calm but at the back of your mind there is the possibility that you might die."
The couple believe they caught the virus on a flight back from Mexico.
They returned to their home on Thursday having been treated for five nights in separate isolation rooms at Monklands Hospital, Airdrie.
"It was particularly hard to bear, because I knew that Dawn was next door and that she wasn't well," Mr Askham told the newspaper.
"She was so close and yet I could not reach her. I just wanted to give her a cuddle and reassure her."
The couple said they believed they contracted the virus on their flight back from Cancun, during which several passengers were coughing and sneezing.
Of the eight cases confirmed in the UK so far, three are in London, there has been one each in Newcastle upon Tyne and Redditch, Worcestershire, and a 12-year-old girl has tested positive in Paignton, Devon.
All of those diagnosed are thought to have responded well to treatment.
Advertising campaign
Precautions being taken in the UK include enhanced airport checks, an expansion of anti-viral stocks from 35 million to 50 million by the end of May, the ordering of extra face masks and delivery of information leaflets for every family.
Supplies of antibiotics are to be increased to deal with any complications arising as a result of flu infections.
An advertising campaign to help prevent the spread of the virus has also been launched.
The Department of Health's Catch it, Bin it, Kill it! adverts urge people to cover coughs and sneezes with tissues, throw them away and wash their hands.
Meanwhile, the WHO has announced it will call the virus influenza A (H1N1), rather than swine flu, which it says is misleading as pork meat is safe and the virus is being transmitted from human to human.
Members of the public with concerns about the virus can call 08454 24 24 24.
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An advertising campaign urges people to catch the sneeze before binning the tissue
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