Sturgeon became the leader of the ruling Scottish National Party after its 2014 independence referendum when the country voted 55 per cent to 45 per cent to remain as part of the United Kingdom.
The BBC cited a source close to Sturgeon as saying "she's had enough".
She will give a news conference at her official residence in Edinburgh at 11am (2200 AEDT) on Wednesday.
Sturgeon suffered a blow in November when the United Kingdom's top court ruled that the Scottish government could not hold a second referendum without approval from the British parliament.
Sturgeon said in response that she would turn the next British general election into a de facto referendum to ramp on pressure on Westminster to grant another vote.
Support for independence rose above 50 per cent in the wake of the Supreme Court ruling but it has slipped back in recent months.
Sturgeon, 52, had also recently become embroiled in a row over transgender policies after Scotland passed a bill to make it easier for people to change their legal gender.
The Conservative government of Prime Minister Rishi Sunak responded by saying it would block the bill, the first time it had invoked the power to veto a Scottish law, because it would have a broader impact on the United Kingdom.
Scotland was then forced to review the management of trans prisoners and stop transgender people with a history of violence against women being placed in female prisons.
Reuters and PA
