A spokesman said the allegations were “nonsense” and that “all sums raised for independence campaigning will be spent on independence campaigning”.
Police Scotland launched a formal investigation into potential criminality involving SNP fundraising earlier this month after receiving complaints.
The probe followed the SNP raising more than £660,000 since 2017 specifically to fight a second referendum campaign.
Questions have been raised about the money after the SNP’s accounts showed it had just under £97,000 in the bank at the end of 2019, and total net assets of about £272,000.
The party has pledged to spend an “equivalent” sum on a second referendum, but refused to formally identify this money in its annual accounts for 2020.
The Sunday Times reported claims that some of the donations may have been spent refurbishing the SNP’s offices near Holyrood, as well as on legal costs relating to the Scottish Parliament’s Alex Salmond inquiry.
An SNP spokesman said: “These claims are nonsense. As we have said before, all sums raised for independence campaigning will be spent on independence campaigning.
“We will fully cooperate with the police investigation, and will make no further comment.”
In March, three members of the SNP’s finance and audit committee quit amid complaints about being denied access to the accounts.
Two months later new SNP treasurer Douglas Chapman MP also quit, complaining a lack of transparency had stopped him carrying out his “fiduciary duties”.
SNP MP Joanna Cherry QC quit the party’s ruling National Executive Committee the same month, again citing issues with transparency.
The First Minister previously said she is “not concerned about the party’s finances”.
She told STV in June: “The finances of the SNP are independently audited, our accounts are sent to the Electoral Commission in common with other parties and of course published, so there’s full scrutiny around that. Money hasn’t gone missing. All money goes through the SNP accounts independently and fully audited.
“Every penny we raise to support the campaign for independence will be spent on the campaign for independence.”
Scottish Conservative Chief Whip Stephen Kerr, MSP said: “The SNP need to come clean about this murky situation once and for all.
“Senior SNP members have resigned over this affair so it is time the First Minister is upfront about what she knows about this funding. It is clear the SNP can’t get their stories straight and are desperately trying to cover their tracks. Scotland’s ruling party are shamefully aiming to pull the wool over the eyes of the public.
“Police are investigating almost 20 fraud complaints and Nicola Sturgeon was aware of concerns over this money two years ago.
“Even their own supporters are furious at this money disappearing into a black hole yet now the SNP leadership have put out the begging bowl again to them.
“The SNP are only continuing to paint Scottish politics in a bad light with this ever increasing sorry affair.”