Speaking to the BBC’s Andrew Marr show on Sunday, the First Minister said that Scottish officials would “take a very close look” at making sure the virus isn’t brought into the country by people arriving from other parts of the UK.
Host Andrew Marr asked Sturgeon: "You have said that the rate of infection of coronavirus in England is now five times worse than Scotland where you're pursuing an elimination strategy and yet you are not pressing the button on people from England coming into Scotland quarantine. Why not?"
"I said we will keep all of these things under review,” Sturgeon replied.
"I set out in Parliament on Thursday is one of our biggest risks in the next weeks is the risk of importation into the country - that's why we've taken a very cautious decision on international quarantine.
“And, this is not a position I relish being in, it also means 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.
“That’s not political, it’s not constitutional, it’s just taking a similar view to countries across the world in terms of protecting populations from the risk of the virus.
“It’s not something we have decided to do at this stage, it’s not something I am immediately planning to do but I will take decisions the best I can to protect the health of Scotland and to take that absolutely from a public health perspective.”
Sturgeon added that all four UK nations need to work together on outbreak management in a way that "mitigates against having to put any border restrictions in place".
She also said she would like to see the government be more explicit that it was trying to get to levels of coronavirus that were "virtually elimination levels".
"We need to be sure that any outbreaks in England are being properly managed just as England will want to be sure that any outbreaks in Scotland are properly managed," she said.
"It's when there isn't that confidence that the concerns about possible importation would grow."
Speaking on Times Radio on Sunday, Cabinet Office minister Michael Gove downplayed the idea of border checks between Scotland and England.
“I don’t think the idea of erecting a hard border between Scotland & England is in any way a good thing,” he said.
“But I don’t want to be unfair to Nicola Sturgeon... I want our governments to work together."