The UK Government said today it was “working rapidly” on the potential measure as part of wider sanctions following Russia’s invasion of Ukraine on Thursday.
It followed Orkney and Shetland Liberal Democrat MP Alistair Carmichael urging Prime Minister Boris Johnson to stop Russian-owned vessels entering UK ports with the Russian shipping firm Sovcomflot’s tanker NS Champion due to arrive at the Flotta terminal in Orkney on Tuesday.
He told the PM: “It is imperative that you should act without delay to ensure that Sovcomflot is sanctioned and denied access for their vessels to British ports.
“Like right-thinking people across the United Kingdom, the people of Orkney have been sickened by what we have seen on our television screens of the Russian attack on Ukraine.
"We expect you, as our Prime Minister, to act to stop this continued trade that is earning money to fund the slaughter of Ukrainian citizens.”
A UK Government spokesperson said: “We are aware of concerns about Russian-connected ships potentially docking in the UK and we are working rapidly to explore a range of measures to restrict access for them.
“We are already discussing this issue with the Scottish Government and the sanctions being considered are part of a wider package being worked up across the UK Government.”
Angus Robertson, Scotland's External Affairs Secretary, told BBC Scotland: "The UK authorities have got a big decision to take, on whether we are going to allow Russian-owned or charted vessels to dock in UK ports.
"The Scottish Government is in discussions with the UK authorities about this particular case but there will be others.
"This is a very fast-moving situation and we're going to have to act, and this is a very good example of an area where we are going to have to act decisively because we can’t carry on as if nothing’s happening on the far side of Europe."
Mr Carmichael said another Sovcomflot tanker, NS Challenger, had just left the Sullom Voe terminal in Shetland.
He said such vessels currently operated freely and could not legally be denied access to ports by local authorities.
The MP also claimed that allowing continued access by Sovcomflot vessels to Orkney would “dishonour the memory of the sacrifice that the crew of the Royal Oak made in their fight against fascism”, in a reference to the sinking of the Royal Navy flagship by a German submarine in Scapa Flow in 1939 with a loss of 835 lives.
In a letter to Mr Johnson, he wrote: “Scapa Flow was at the centre of the UK’s naval effort in two world wars in the 20th century.
"That remains a source of pride in our community to this day.
"It is also the final resting place of many of the 835 men and boys who lost their lives on 14 October 1939 when their ship, HMS Royal Oak, was torpedoed by a German U-Boat."
Forth Ports, which includes Leith, Grangemouth, Rosyth and Dundee, said no Russian ships were due to visit.
Peel Ports, which includes Greenock and Glasgow, said there were "no known Russian vessels in or arriving at" its ports.