The BBC says it understands that people in Scotland will be able to travel to some international destinations without having to quarantine on their return.
The move is meant to be part of a ‘traffic lights’ system which is supposed to be implemented on May 24.
Countries will be classified as green, amber and red. Those in the green category will require self-isolation.
A Scottish Government Covid briefing held by Nicola Sturgeon will take place on Tuesday just after midday.
Ms Sturgeon is expected to announce the next steps in Scotland’s exit out of lockdown.
The UK Government also repeated the Transport Secretary’s announcement that international travel can begin to safely reopen from May 17, allowing people from England to go on foreign holidays to “green” list countries.
This includes Portugal, Gibraltar, Israel, Australia, New Zealand, Singapore, Brunei, Iceland and the Faroe Islands, as well as several small remote islands that are British Overseas Territories.
Strict border control measures will remain in place, including pre-departure tests and a PCR test on or before day two of arriving back in the UK.
It came as Boris Johnson announced an easing of restrictions in England from next Monday and hailed it as a “considerable step on the road map back to normality”.
The Prime Minister told a Downing Street press conference the UK Government remained on “track” to end all restrictions by June 21 and thanked the public for their efforts.
He said: “I want to thank you particularly because your efforts have so visibly paid off, giving us the time to vaccinate more than two thirds of all adults across the UK, with more than one third – nearly 18 million people – also receiving their second dose and thereby unquestionably saving many lives.
“And so it’s precisely because of your efforts that I can confirm that we’ve met our four tests for further easing the lockdown in England.”
The relaxing of restrictions comes amid a significant decline in Covid cases, with just two related deaths having been recorded in Scotland so far this month.
On Sunday there were 287,797 vaccines in the UK, with 11,181 first doses in Scotland, and 17,000 second jabs.
Scotland recorded 168 new cases of coronavirus.
This means from Monday family and friends will be able to hug as well as meet indoors south of the border.
His announcement came during a press conference that also saw England’s chief medical officer Professor Chris Whitty warn the variant first detected in India is one “we need to keep quite a close eye on”.
He said: “This is actually spreading from very small amounts, but it is beginning to spread in certain parts of the country and we need to keep quite a close eye on this.
“So the point about this is the threats are significantly reduced, but there are still some residual issues that we need to keep a very close eye on and therefore we need to go carefully and steadily, as the Prime Minister has said.”
Mr Johnson also dodged a question as to when it would be safe to hold a second independence referendum.
He answered: “I had good conversations with all the heads of the devolved administrations and everyone was resolved that the number one priority for the whole of the UK was to come out of the coronavirus pandemic and build back better.”