Mr Swinney, who is also Cabinet secretary for the Covid recovery, was pressed on BBC Scotland’s Sunday Show about the money and the resignation of MP Douglas Chapman as the party’s National Executive Committee (NEC) treasurer on Saturday night.
Asked if the police were looking into missing party funds, Mr Swinney said: “Not to my knowledge.”
On the resignation of Mr Chapman – which was announced on Twitter on Saturday night – Mr Swinney added: “I’m aware of that. I don't understand what has prompted this. Our NEC has responsibility for scrutinising party finances and I saw that point was confirmed on social media last night.
"In addition to that, the accounts are independently audited by external auditors and submitted to the Electoral Commission for scrutiny. There’s a huge amount of scrutiny of party finances that go on. That happens daily within the SNP and so it should.”
Pressed again on whether there was a police investigation underway, he reiterated: “Not to my knowledge.”
In March three members of the party’s finance and audit committee resigned after the First Minister’s husband and party chief executive Peter Murrell reportedly refused to show them accounts.
Police Scotland has confirmed that is is assessing a complaint of fraud against the party to determine if a full investigation should be carried out. It is alleged that money raised by activists to prepare for another independence referendum has been diverted.
The force said it had received an allegation of fraud – after a complaint by independence activist Sean Clerkin – and inquiries were ongoing. A second activist, David Henry, also told Edinburgh Sheriff Court on Friday that detectives had visited him in connection with their probe.
A Police Scotland spokesperson said: “The complaint is still being assessed to determine if an investigation is required.”
However events took another twist with Mr Chapman’s resignation.
On Twitter he said: “Despite having a resounding mandate from members to introduce more transparency into the party's finances, I have not received the support or financial information to carry out the fiduciary duties of National Treasurer. Regretfully I have resigned with immediate effect.”
Scottish Conservative chief whip Stephen Kerr said on Sunday it “spoke volumes” that Mr Chapman was unable to “get the party to open the books”.
He added: "There are obvious questions the leadership have yet to answer for members and even their own politicians. But even simple pleas for transparency have further opened up the rift between the nationalists.”
And Scottish Labour’s deputy leader Jackie Baillie said: “Douglas Chapman’s extraordinary resignation makes it essential that the SNP are open about the growing number of questions about their finances.
“There are clearly issues that need to be looked at within the secretive inner workings and inner circle that runs the SNP. Nicola Sturgeon must agree to open the party’s books to public scrutiny so investigators can get to the bottom of this mess.”
SNP business convener and fellow MP Kirsten Oswald said she fundamentally disagreed with Mr Chapman's assessment.
She said: "However, I respect his decision, thank him for his contribution to the NEC and wish him well."