Some 800,000 people who were born in Scotland now live in England, with a further 50,000 resident in Wales.
The majority of Scots living outside Scotland are thought to support the Union.
Polling guru Sir John Curtice has suggested their inclusion in a second referendum could hand victory to the No vote while opinions on independence inside Scotland remains almost evenly split.
‘It’s going to happen’
Reacting to the news on Monday morning, the First Minister told followers on Twitter: “I see the anti independence campaign is trying to rig the rules of #indyref2 again (tho in doing so they also concede that it’s going to happen).
“Maybe they should just argue their case on its merits and allow everyone who lives in Scotland to decide,” she added.
Senior Conservatives pushing for the rule change compare the proposal to the decision to allow expatriate Brits to vote in the 2016 EU referendum.
But a similar proposal to allow Scots living in other parts of the UK to vote was debated in the negotiations ahead of the first independence referendum in 2014 - and was rejected outright by the SNP.
Any attempts to impose the rule change for a future vote on the Union would likely face similar resistance.
The news comes as the Prime Minister Boris Johnson faces mounting pressure to counter the SNP after their historic victory in the Holyrood elections last month.
No. 10’s so-called “Union unit” has been mired in crisis after losing two appointed leaders in a matter of weeks, and being described earlier this year as a focal-point of “Whitehall psychodrama”.
Mr Johnson has also been urged to appoint Ruth Davidson to a newly created role of constitutional secretary.
The position would make Ms Davidson, who stepped down as leader of the Scottish Conservatives in 2019, the de-facto chief of any future pro-Union campaign.