First Minister Nicola Sturgeon has said any move to place restrictions on visitors from England to Scotland would be based on risk, not politics.
Speaking on The Andrew Marr Show, she said quarantine for visitors from elsewhere in the UK could not be ruled out.
Prime Minister Boris Johnson has previously called the idea "astonishing and shameful".
Scotland has been recording a lower rate of Covid infections than England.
Figures released on Sunday indicated that 19 people had tested positive for the virus in Scotland in the previous 24 hours.
This is the highest figure for three weeks.
But for the fourth consecutive day, no deaths were recorded.
The first minister said the UK nations need to work together on outbreak management in a way that "mitigates against having to put any border restrictions in place".
Ms Sturgeon told Andrew Marr: "One of our biggest risks over the next few weeks, as we have driven levels of the virus to very low levels in Scotland, is the risk of importation into the country.
"That's why we've taken a very cautious decision about international quarantine.
"And - this is not a position I relish being in - it also means that we have to take a very close look at making sure that we are not seeing the virus come in from other parts of the UK."
The first minister pointed out that in countries such as Australia and the United States, controls have been put in place to limit movement across state or regional boundaries.
The Scottish government would look at similar measures on a public health basis.
Ms Sturgeon said: "That's not political. It's not constitutional. It's just taking a similar view to countries across the world in terms of protecting the population from the risk of the virus."
"This is not about saying to people in England you are not welcome in Scotland - of course people in England are welcome in Scotland," she added.
The topic of quarantine for visitors from England entering Scotland was raised at Prime Minister's Questions, with Mr Johnson describing the idea as "astonishing and shameful".
He added: "There have been no such discussions with the Scottish administration about that, but I would point out that there is no such thing as a border between England and Scotland."
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