But politicians and tourism groups in Berwickshire are warning such a move could create chaos in the area – and have a massive impact on the economy.
The petition calls on the UK Government to give the devolved nations the right to close their borders should infection rates in England be much higher.
As of yesterday, more than 8,000 people had signed the petition on Change.org.
First Minister Nicola Sturgeon has said she has “no plans to introduce anything like this just now” – but she refused to rule anything out.
The possibility of the border being closed has appalled Berwickshire’s Conservative MSP and MP.
Rachael Hamilton MSP stressed that Nicola Sturgeon does not have the power to close the border.
She added: “This is totally impractical and economically unviable – key workers from Cornhill-on-Tweed work in Kelso, people from Berwick-upon-Tweed take employment in Eyemouth.
“Any attempt to close the border would wreak havoc on a Borders economy that is trying to restart after weeks of lockdown.
“People who want to close the border fail to realise that cases are increasing and decreasing in different areas of Scotland and England. Neighbouring Northumberland isn’t any worse than the Borders.
“There are more cases of coronavirus in Edinburgh than the Borders, but we don’t stop travel between the two.
“We must realise that this nationalist petition on closing the border would damage the Borders and Scottish economy even further.”
John Lamont MP was equally critical of any move to close the border between Scotland and England.
He said: “For many people in Berwickshire and Northumberland, going across the border is a part of everyday life.
“People go to work, do their food shopping and go to school on the opposite side to where they live.
“Closing it would cause huge problems for people that cross it every day.
“This is not to mention the disruption it would cause for the thousands of lorries that keep our shelves stocked and our businesses trading.”
The Scottish Tourism Alliance (STA) has also reacted with concern, fearing that such a move could have a detrimental impact on the industry’s recovery.
Marc Crothall, STA chief executive welcomed further confirmation on Monday from the Finance Secretary Kate Forbes that the Scottish Government has no intention as it stands to impose such a quarantine restriction on those visiting from England.
“Let’s hope that the virus does not spread in such a way that it requires the Scottish Government to reconsider this status,” he said.
Mr Crothall added: “Clearly given that over 70 per cent of Scottish tourism comes from the UK market, any restrictions on domestic travel will have a significantly negative impact on the sector.
“In fact, I know of a few businesses who have received enquiries from people south of the border who have become concerned about a potential quarantine and have asked for reassurance of a full refund should a quarantine come into force.”
While stressing there are no plans for a border closure at this time, Ms Sturgeon said that if there was an ongoing divergence between infection rates in Scotland and other parts of the UK, the government would need to see how to mitigate that and guard against infection rates rising in Scotland as a result.