John Swinney has said the SNP needed "fresh perspective" on how to build support for Scottish independence.
The Deputy First Minister - who ruled himself out as a replacement for Nicola Sturgeon last night - poured scorn on the suggestion that members who left over the last year should be readmitted.
He said it would be "preposterous" to let former SNP members back into the party to vote in the election to find a new party leader.
The SNP’s governing body has said the race for a new leader will last less than six weeks, while its special conference to discuss the way forward for Scottish independence has been postponed.
So far no candidates have officially declared themselves - but as the Record revealed last night, Health Secretary Humza Yousaf is expected to announce he is running to become Scotland’s next First Minister.
Swinney said his party needed "fresh perspective" on how to build support for Scottish independence.
The MSP, who is a former leader of the party, said: “Independence cannot be some abstract concept, it has to be a means of addressing the issues that matter to the people of Scotland.”
He was asked if SNP members who left in opposition to its policy on gender recognition reform would be allowed back into the party to vote in this contest.
Ash Regan, a former Scottish Government minister who quit her frontbench role in protest over the policy, has called for members who left over the last year to be readmitted.
Swinney said: “It would be an absolutely ludicrous proposition that you open your membership lists when you’ve got a major vacancy of this type. It’s just preposterous.”
He was also asked about a tweet from Regan on Friday morning, where she said SNP MPs should be allowed to stand in Holyrood elections.
Swinney pointed out that Scottish Government minister Neil Gray gave up his Westminster seat in order to successfully run for the Scottish Parliament.
Asked about whether there would be a Scottish election once the new leader is in place, he said Holyrood operated on a fixed-term basis and the situation is “very different” to the one caused by Liz Truss as Prime Minister.
After a meeting of the party’s national executive committee, those eying the top job have until February 24 to submit their nomination, with the vote open between March 13 and 27.
Lorna Finn, the party’s national secretary, said on Thursday: “Nicola (Sturgeon) has been the outstanding politician of this generation.
“We are very fortunate that she will remain an SNP MSP and a leading campaigner for an independent Scotland.
“But the SNP is full of talented individuals and they now have the opportunity to put themselves forward and our new leader will lead us into the final phase of Scotland’s journey towards independence.”
The results of the contest will be made public as soon as the result is determined, the party said, and after the candidates have been told.
The Record revealed last night how Yousaf was expected to announce his bid to become the next leader of the SNP.
We told how a close pal of the Health Secretary had "a lot of support from MPs and MSPs" and labelled him a "unifying force" who had experience having been in government for a decade.
"Just as he has managed to get health unions round the table, he would bring the party together," they added.
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