According to the Sunday Times the party's treasurer told its ruling body it was struggling to balance the books due to an exodus of members and donors.
The SNP told the BBC selective quotes had been taken out of context.
On Saturday the new leader Humza Yousaf dismissed rumours the SNP faced bankruptcy, saying the party was solvent.
The SNP's National Executive Committee (NEC) met on Saturday morning following a turbulent fortnight which has seen the arrest of former chief executive Peter Murrell and the SNP's offices searched by police.
When Mr Yousaf later faced questions about rumours the party was facing possible bankruptcy, he replied: "It's not. The party is solvent."
However, the Sunday Times reported that the NEC meeting had been told by party treasurer Colin Beattie that it was "having difficulty in balancing the books due to the reduction in membership and donors".
He also warned that a likely Westminster by-election in Rutherglen and Hamilton West in the coming months could "put the party under pressure", according to the paper.
The SNP said the report was misleading and insisted the party was ready to contest any possible by-election which could be triggered if MP Margaret Ferrier is suspended from the Commons for breaching Covid rules.
"Selected quotes being pulled out of context are not an accurate representation of the case presented at today's [Saturday's] meeting of the party's National Executive Committee," a spokesperson said.
"The SNP's National Treasurer confirmed the party's finances are in balance and, as Scotland's largest political party, we will fight any by-election with the intention to win - to suggest otherwise is farcical."
Meanwhile, the party's former Westminster leader Ian Blackford also insisted there was no immediate threat to the party's finances.
Asked if the party was solvent Mr Blackford told The Sunday Show on Radio Scotland: "Absolutely, categorically, the SNP is solvent.
"The finances are in balance. We will be able to meet our obligations and liabilities going forward."
The Ross, Skye and Lochaber MP acknowledged there had been "a dip" in membership but added he was optimistic the party would be able to reverse the decline.
He added: "When all is said and done we have still got over 70,000 members, members that are paying subscriptions, donations coming in, parliamentarians making contributions.
"As would be normal we will be looking at how we can raise additional funds as well.
"But the party will be ready to meet all its liabilities and will certainly be ready to meet the challenge, if it comes, of a by-election in Rutherglen over the coming period."
Last week, Mr Yousaf revealed that he had been unaware until he became leader that the SNP's auditors had resigned more than six months ago.
The firm Johnston Carmichael quit last September, and there is concern the party may be unable to conduct an audit due in July. The party has acknowledged difficulties in recruiting new auditors.
On Thursday, the new SNP leader and first minister also said he only recently learned that the SNP had bought a luxury motorhome.
It was seized by police from outside a property in Dunfermline as part of the police investigation into the party's finances.
According to Daily Record it was bought as a campaign bus ahead of the 2021 Holyrood election in case Covid restrictions limited other forms of social mixing - but was never used.
Former SNP chief executive Peter Murrell, who is Nicola Sturgeon's husband, was arrested on 5 April while their home and the SNP's Edinburgh offices were searched as part of the police investigation. He was later released without charge pending further inquiries.
Mr Murrell resigned from his SNP position last month after misleading statements about party membership numbers were given to a journalist.
The police investigation follows complaints about how the party spent more than £600,000 of donations that it received from activists to fund a future independence referendum campaign.
Questions were raised after accounts showed the SNP had just under £97,000 in the bank at the end of 2019, and total net assets of about £272,000.
On Saturday the party's NEC approved proposals for an internal review of governance and transparency, as well as the appointment of a new chief executive through an "open and transparent" external recruitment process.
Prior to the NEC meeting, one committee member had suggested he might resign unless "forensic auditors" were appointed to examine the party's finances.
Bill Ramsay, the SNP trade union group convener, said: "I have been raising issues about the governance of the party for some time."
A forensic audit is a term often used to described an audit aimed at uncovering evidence that could be presented in a court of law.
Humza Yousaf later said a resolution passed unanimously at the NEC meeting referred to "external input" into the review - which could include forensic auditors.
Scottish Conservative chairman Craig Hoy questioned why the party had not yet appointed new auditors.
He said: "People inside and outside the SNP are sick and tired of senior figures' secrecy and lack of transparency."
And Scottish Labour's Jackie Baille said: "The SNP is a party in complete disarray - with claim and counter-claim being traded in the crossfire."
Mr Yousaf was campaigning in the Rutherglen and Hamilton West constituency on Saturday, where there is the prospect of a Westminster by-election.
Margaret Ferrier won the seat for the SNP in 2019 - but was later found to have damaged the reputation of the Commons and placed people at risk by taking part in a debate and travelling by train after testing positive for Covid-19. She now sits as an independent.
If she is barred from the Commons for 10 days or more, that could trigger a recall petition, which would result in a by-election in the constituency - although 10% of voters there would need to support this for it to go ahead.