The First Minister said the prospect of enhanced measures would be "important" amid growing concerns about the virulence of a new South African strain of the virus.
Anyone travelling to the UK could be required to produce a negative Covid-19 test no more than 72 hours before their journey, reports have suggested.
Ms Sturgeon told Tuesday’s coronavirus briefing she has discussed the prospect of new border controls with UK leaders.
"I had a four-nations discussion last night, chaired by Michael Gove from the UK Government, where the issue of borders, stricter restrictions on travel and controls at the border was discussed," she said.
"There was an agreement in that call to take forward some urgent four-nations discussions about that over the course of the days.”
She added: "I do think that is important and when it comes to border controls, the border force is not a responsibility of the Scottish Government, but there is, I hope, a willingness to be collaborative in how we make these decisions.”
The SNP leader also made it clear that existing rules effectively bar travel in and out of Scotland for non-essential reasons.
She said: "I want to stress something that is perhaps just still not well enough understood, which is my responsibility in my role if that is the case, that it is against the law now to travel outside of Scotland or into Scotland without it being for an essential purpose.
“You should not be going overseas unless it is essential and you should not be coming into Scotland unless it is essential. That's different to actual physical control of the border, but that's the legal position.
"We have effectively said travel is banned and that is a message that I want to get across there very seriously."
But international arrivals into Scotland represent a "very, very small" fraction of what these were a year ago, the First Minister said.
"International travel has really plummeted and that's certainly important and we want to make sure that we're not allowing new strains of the virus into the country," she said.
National clinical director Professor Jason Leitch said there were "hundreds of different mutations" of the virus around the world.
He said it remained unknown whether the vaccine would work on the South African variant of the virus, but "there is no reason to think it won't”.
The strain is being grown at the Ministry of Defence's Defence Science and Technology Laboratory (DSTL) at Porton Down for testing to be carried out.
The tightening of rules follows criticism of the lack of screening of international arrivals.
Mr Gove said UK ministers would make announcements in the days ahead about measures to “make sure that our ports and airports are safe”.
He said: “It is already the case that there are significant restrictions on people coming into this country and, of course, we’re stressing that nobody should be travelling abroad.”