Two of the three candidates vying to be leader of the SNP want an independent auditor to oversee the leadership vote.
Kate Forbes' campaign manager, MSP Michelle Thomson, said concerns had been raised about the integrity of the ballot process.
Ash Regan's spokesman said an auditor would give reassurance to party members and the public.
The SNP is expected to release its membership figures today after demands from all three in the contest.
It previously said it would only give the numbers when the result of the vote was announced.
On Thursday Ash Regan called for transparency in an open letter, also written on behalf of Kate Forbes, to SNP chief executive officer Peter Murrell.
The BBC says candidate Humza Yousaf's team said he had "sought assurances" figures would be released.
Mr Murrell, who is Nicola Sturgeon's husband, was urged to clarify "paid-up" party member numbers, and the number of digital and postal voting papers that had been released.