Transport Minister Keith Brown wants SNP rules changed so new members are given a say in choosing the party’s candidates for the general election next year.
The MSP for Clackmannanshire and Dunblane said it was important to involve the party’s growing army of supporters in the process.
Current party rules state that people have to have been a member for at least 13 months before their voice is heard.
But Mr Brown, who hopes to be the SNP’s next deputy leader, claimed the party was facing “exceptional circumstances” and an exception should be made.
The minister has raised the issue with SNP business convener Derek Mackay.
Mr Brown said: “We’ve seen enormous numbers of people joining the SNP since the referendum, nearly 50,000 at the last count.
“They joined in good faith with a commitment to fulfilling the SNP’s long-term ambitions for Scotland.
“It would be less than welcoming if the party did not do everything we could to make sure that they have a say in the first round of selections after they have joined.
“We’re going to have to change party structures to give all of the new members a chance to make their contribution to the SNP in the longer term and we may as well start with this measure to allow them all a say in choosing our candidates for next year.”