The paper has reported that Scottish Government sources say there is fear that the tourism season could undo the progress Scotland has made in suppressing the virus.
It is understood visitors from England could be told to go into quarantine for two weeks or face a fine if cases of Covid-19 south of the border rise again.
At the end of last week, the First Minister said Scotland was nearing ‘total elimination’ of the virus.
There have now been no new deaths for a third day in a row.
Today, Edinburgh University’s Professor Devi Sridhar said Scotland could be free of coronavirus by the end of the summer.
She told the BBC, that as long as cases stayed at a low level, and contact tracing was effective: "I think for me that's pretty much a Covid-free Scotland.
“At that point the risk to people's daily lives becomes negligible.”
Confirmed cases of Covid-19 continued to rise in England last week.
The full article in The Sunday Times can be read here.
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