One Westminster parliamentarian said it was a “matter for events” if the SNP leader remained in post.
The SNP leader has also come under fire from some in her party over her government's strategy to secure a second independence referendum, which she continues to insist can take place this year despite Boris Johnson's refusal to grant the legal powers to hold a vote.
Asked what he thought about SNP colleagues privately raising questions over Ms Sturgeon’s future, Western Isles MP Angus MacNeil told the BBC: "I suppose that's maybe a matter for events and Nicola Sturgeon - who knows?
“What I'm concentrating on is not so much the personalities involved but it's the issue of independence."
A second MP, East Lothian’s Kenny Macaskill - who served in Mr Salmond’s cabinet alongside Ms Sturgeon - also failed to give the SNP leader his full-throated support, saying: “There is no vacancy."
Mr Macaskill went on: “You never say never in politics - but at the present moment there is no challenge in the SNP, nobody seeks it, we're comfortable with Nicola's leadership.
“We'll see what happens but she still has a lot of fuel in the tank.”
The comments have already provoked public divisions in the SNP, with Justice Secretary Humza Yousaf posting on twitter: "The couple of MPs stirring the pot & trying to disrupt are doing themselves & the Independence cause no good whatsoever."
“We take absolutely nothing for granted, and will continue to work hard to retain the trust of the people of Scotland."