The separatist leaders will write to the First Minister, seeing him as a potential Western ally who understands their desire to break away from a larger state.
At a press conference in Moscow, separatist official Andrei Kramar said: "We hope he will explain to the West in plain English why the Donetsk and Luhansk regions have taken this step."
Mr Kramar, who presented himself as one of two Russian representatives of the newly formed Donetsk People's Republic, acknowledged that the circumstances of south-east Ukraine and Scotland were different, but he added: "Scotland will understand."
Mr Kramar also revealed that the Donetsk People's Republic leadership had made plans to ask other leaders around the world for recognition and support.
Separatists in Donetsk and Luhansk claimed 89% and 96% respectively voted in favour of self-rule in the referendums.
But Olexander Turchynov, Ukraine's acting president, said the claimed turnout of 75% by the rebels was nearer 30%.
He told Ukraine's parliament: "The farce that terrorist separatists call a referendum is nothing more than propaganda to cover up murders, kidnappings, violence and other serious crimes."
The move by the pro-Russian separatists to try to engage Mr Salmond in their cause will do little to ease the controversy sparked by the FM's recent remarks in a magazine interview last month.
In GQ magazine he admitted to admiring "certain aspects" of Russian President Vladimir Putin and praised him for restoring "a substantial part of Russian pride."
The SNP leader's political opponents seized on the comments, with Prime Minister David Cameron accusing Mr Salmond of "a major error of judgment".
The First Minister is due to meet with Scottish Ukrainians shortly to explain his comments but last night Willie Rennie, the Scottish Liberal Democrat leader, renewed his call for the SNP leader to apologise. He said: "The fact that pro-Russian separatists in the Ukraine now appear to view the First Minister as some sort of poster-boy for their cause would suggest he has failed to convince people his comments on President Putin were balanced.
"Alex Salmond now needs to do what he should have done in the first place, which is apologise for his ill-judged remarks."
In response, a Scottish Government spokeswoman said: "It is internationally recognised that the referenda being held in Ukraine are unconstitutional, illegal and illegitimate, and the Scottish Government has consistently made clear we agree with that view.
"In contrast, Scotland's forthcoming referendum has been agreed as part of a legal and constitutional process, culminating in the Edinburgh Agreement.
"Scotland's referendum has been cited internationally, including by US Secretary of State John Kerry, as a model of how such processes should be conducted."
Meanwhile the Prime Minister told MPs Britain was to offer another two Typhoon warplanes to patrol the skies of eastern Europe amid continuing tensions with Russia over Ukraine.
The RAF has already sent four Typhoons to join Nato's air policing mission over its Baltic member countries of Estonia, Latvia and Lithuania.