SNP leader Sturgeon has previously said there could only be another independence vote if Scots voted for a party which proposed one in a Scottish parliamentary election.
Scottish elections are due in May 2016 but so far Sturgeon has refused to say directly whether she would include a referendum pledge in her manifesto.
After Jeremy Corbyn was elected as the new leader of the opposition Labour Party on Saturday, Sturgeon cautioned that if his party failed to show swiftly it could beat Cameron's Conservatives in the next national election then desire for Scottish independence would rise.
"If Labour cannot quickly demonstrate that they have a credible chance of winning the next UK general election, many more people in Scotland are likely to conclude that independence is the only alternative to continued Tory (Conservative)government," she said.
"The reality today is that at a time when the country needs strong opposition to the Tories, Jeremy Corbyn leads a deeply, and very bitterly, divided party."
Sturgeon has previously warned that if England voted to leave the European Union in a referendum on membership due by the end of 2017, then Scotland could seek a second independence referendum if its people voted to stay in the EU.