The Edinburgh South West MP has insisted no woman should ever "write herself off" as a potential leader, but admitted she is fed up with speculation touting her as a successor to Nicola Sturgeon
Any SNP leader must be based an MSP at Holyrood, she added.
Ms Cherry, the party's Home Affairs spokeswoman at Westminster has become one of the most high profile politicians in the UK after her leading role in the successful court challenge which saw the UK Government's recent prorogation of Parliament ruled unlawful and overturned.
Ms Sturgeon has made it clear that she intends to lead the party into the next Holyrood elections in 2021, but Ms Cherry hinted that she may be a contender for the top in the longer term.
"I wouldn’t rule myself out for the future," Ms Cherry said in an interview with Holyrood magazine.
"But there is no leadership vacancy right now and I’m not putting myself forward as a potential leader of the SNP at the moment. Those who are doing so are mentioning my name without my involvement or my permission.”
Ms Cherry insisted she would love to play a "leadership role" in a future independent Scotland.
"No woman should ever write herself off as a potential leader," Ms Cherry added.
"I’ve worked very hard in my role and I know I’ve got quite a big public profile now and I’m popular with the party membership, but there isn’t a vacancy for an SNP leader.
"We have a very strong and effective leader and there’s no vacancy. Moreover, the speculation that I will or might challenge is a set-up by journalists. It’s ridiculous. I’m at Westminster, the leader of the SNP must be at Holyrood, because they must be capable of being first minister, and I have never said I want to be party leader; others have said it and frankly, I wish they wouldn’t, because it just causes me grief I could do without.”