James Dornan announced via social media that he was seeking nominations for the position which was vacated by Angus Robertson on Saturday.
The MSP for Cathcart is the first SNP member to publicly announce plans to stand for the role since Mr Robertson stood down, eight months after losing his seat at the general election.
“I would like to announce that I will be seeking nominations for the position of Depute Leader for the Scottish National Party, when the process commences,” he said in a tweet.
Mr Dornan, a former Glasgow City councillor, was elected to the Scottish Parliament in 2011 and is the convener of Holyrood’s Education and Skills Committee.
His candidacy follows warnings from some SNP members the party required a strong deputy leader capable of standing up to Nicola Sturgeon.
Ian Blackford, the Nationalist leader at Westminster, emerged over the weekend as the strong favourite to replace Angus Robertson.
But some in the party are against an effective ‘coronation’ which could see no SNP heavyweights standing against the MP for Ross, Skye and Lochaber.
“The position of deputy has been a non-role since Nicola held it,” a senior SNP source told The Times. “She needs a reshuffle badly, and to be surrounded by people with strong politics, not people who fear her. Our Holyrood intake is a group of lovely people, but frankly a group of political lightweights.”
Mr Blackford has yet to make a formal announcment on whether he will stand for the role, saying he needed time to “reflect with colleagues”.
SNP MSP Alex Neil, a former cabinet minister, has called for an open contest in which the future direction of the party could be debated.
“My view is the more the merrier,” he told the newspaper. “It’s better to have a compeition and a proper debate, and there is a debate to be had about where we go from here, and give us a choice.”
Mr Robertson announced he was stepping down from the role with immediate effect on Saturday, eight months after he lost his Moray seat at June’s general election.
He said he was “tremendously honoured” to have served as Nicola Sturgeon’s number two in the party, telling the Scottish First Minister he valued her “friendship, professional and personal support”.