The SNP has been rocked by the arrest of former chief executive Peter Murrell and current treasurer Colin Beattie, both of whom were later released without charge pending further enquiries.
One senior SNP figure told The Independent it was likely that Ms Sturgeon would also be arrested, given that she is one of the three names believed to be on party accounts.
Ms Sturgeon, Mr Murrell and Mr Beattie were named on the financial information presented to the SNP conference last year, the source said – but added that the police would want to “cover their bases” before any arrest.
On Tuesday, Police Scotland arrested Mr Beattie, who is also an MSP, as part of their investigation into how more than £660,000 in donations, earmarked for an independence referendum, had been used.
Some of the party’s MPs and MSPs have also said it is “inevitable” that Ms Sturgeon will be interviewed by police under caution in the weeks ahead.
One SNP politician told The Times: “Nicola must be next to be interviewed, it’s inevitable,” with another saying: “It’s obvious there’s a list and Nicola’s name is on it.”
A third told the newspaper: “They’ve interviewed witnesses, and now they are onto suspects. It was the small fry, and now it’s the big people – it’s the way the police work.”
The leader of the SNP, Humza Yousaf, who was recently elected to replace Ms Sturgeon, is facing calls to suspend the former leader’s membership of the party along with that of her husband and Mr Beattie.
Following Mr Beattie’s arrest on Tuesday, Mr Yousaf said that he does “not believe” the party is operating in a criminal way, and resisted calls to suspend Mr Beattie from his role as treasurer.
Mr Yousaf said he wanted to discuss “pertinent issues” with Mr Beattie – who was last night released without charge pending further investigation – and said: “People are innocent until proven guilty.”
Kate Forbes, one of the two defeated leadership candidates, said Mr Yousaf needs to take “decisive and quick action” or the party will be in trouble at the next general election.
She told BBC Radio 4 that claims about the party’s finances had been “mind-blowing”, adding that “people are watching with astonishment, but they want to see leadership in dealing with it and resolving it”.
She said: “I think we need decisive and quick action or we will be in trouble ... We perhaps have the next election in the early part of next year. They will vote in that election on the basis of how we have sorted out our internal problems.”
Her fellow leadership candidate Ash Regan appeared to go further, telling the BBC that any SNP members “involved” in the police investigation should be suspended – though she clarified that they would have to be found guilty of “wrongdoing”.
Police Scotland detectives investigating the party’s finances have been handed emails showing that Ms Sturgeon quashed the idea of appointing a fundraising manager in June 2021, according to Scotland’s Sunday Mail.
The newspaper also published a video in which Ms Sturgeon is seen giving officials on the SNP’s national executive committee a stern warning to be “very careful” about suggesting there were “any problems” with party accounts.
Craig Hoy, the chair of the Scottish Conservatives, said: “[Mr Yousaf] must show some leadership and suspend Colin Beattie – along with Peter Murrell and Nicola Sturgeon.”
The Tory chair added: “Colin Beattie should also stand down from membership of the public audit committee until the conclusion of the investigation.”
The Independent has approached the SNP for comment.