Lawyers at Levy and McRae have written to Deputy First Minister John Swinney and senior civil servant Lesley Fraser on the issue.
Separately, they have also contacted members of the committee set up to investigate the Scottish Government's bungled handling of harassment allegations against the former first minister, appealing to them for help as well.
Lawyer David McKie told members of the Committee on the Scottish Government Handling of Harassment Complaints: "It cannot be fair that our client has been left to fund this personally when both the inquiry and the Scottish Government have legal support provided by the public purse".
It comes as MSPs on the committee continue their efforts to have legal documents handed over to them, with ministers so far resisting all calls to do so.
Mr McKie said many of the documents now being discussed "have never been produced or seen by us or by our client previously", adding there is "significant documentation which our client wishes to discuss with us and on which he requires to take legal advice".
But he said Mr Salmond, who raised more than £100,000 in a crowdfunding campaign to help with the costs of his legal challenge against the Scottish Government, has been "put at a significant financial disadvantage in this whole process".
The former first minister was awarded £512,250 after the Court of Session ruled the Scottish Government's handling of the allegations was unlawful.
Mr McKie, in a letter released by the Holyrood committee, stressed the former SNP leader was "a private citizen" who had "already incurred significant personal expense".
The lawyer told Mr Swinney and Ms Fraser: "He does not, like you, have the benefit of a publicly funded legal department.
"He does not have access to the advice of counsel paid for by the taxpayer.
"The inequality of arms is stark."
As a result, he added Mr Salmond "requires assistance on funding" to enable him to take legal advice on these documents.