While broadcast licensing is in the hands of the independent regulator Ofcom, RT and the Kremlin-backed news agency Sputnik, which has its UK headquarters in Edinburgh, could both be hit by sanctions on Wednesday as part of a crackdown over the Salisbury attack.
The Liberal Democrat MSP Alex Cole-Hamilton called the former First Minister a "useful idiot" for the Putin government and demanded he quit the broadcaster.
“In the space of a week we’ve seen Vladimir Putin fan anti-Semitism by blaming US election meddling on the Russian jewish community and the nerve agent used in a murder plot on British soil traced back to Russian labs," Mr Cole-Hamilton said.
“If even a Prime Minister who has faced criticism in recent months over members of her party ‘taking the ruble’ can call this out, then why can’t our former First Minister?’
‘Alex Salmond has claimed he has editorial control of his show. If that is true he should condemn these developments.
“Salmond has played the useful (and well paid) idiot in RT’s veneer of respectability for long enough.”
Repeated requests to Mr Salmond's representatives in the past 24 hours have not received a response. However, while hosting a radio programme on the LBC network on Sunday, Mr Salmond defended his involvement with the Russian broadcaster by comparing it with the BBC, saying: "I can absolutely assure you that RT was not responsible for the poisoning in Salisbury".
Mr Salmond added: “To make the connection by extension, that someone shouldn’t appear... on a programme which is independently produced and broadcast on a station, which is licensed by Ofcom, and therefore by definition, cannot be a propaganda channel, seems a remarkable extension.
"It is rather like saying that they won’t appear on the BBC, because the British government are selling arms to Saudi Arabia, and bombing helpless people in the Yemen, as the Saudi Arabians are.”
Asked on Monday whether it was appropriate for Mr Salmond to continue producing a programme for RT, the SNP sidestepped the issue, providing a comment from their foreign affairs spokesman at Westminster, Stephen Gethins, who said: "I do not think it is right for MPs to go on Russia Today and take a payment for doing so - and that is something that sitting parliamentarians should think on."
Another SNP MP, Stewart McDonald said any move to ban RT in the UK would be a "retrograde step" as it would encourage the Kremlin to ban western broadcasters like the BBC World Service.
"I am no admirer of Russia Today and have never appeared on its programmes but... closing down RT may well lead to the Russian Government closing the BBC World Service in Russia. That would be a retrograde step," Mr McDonald posted on Twitter.