Detectives investigating SNP finances are said to be searching for sim cards from “burner” mobile phones that are often used to stay anonymous.
Police Scotland officers want to examine information from sim cards which are commonly used in the untraceable phones, according the Sunday Mail.
The newspaper said the purchase of luxury pens, designer kitchenware and even a fridge freezer by SNP officials is also being scrutinised as part of the ongoing probe.
Nicola Sturgeon’s husband Peter Murrell and ex-treasurer Colin Beattie have been arrested and interviewed by police under caution before being released without charge.
Operation Branchform was launched as police inquiry into how more than £660,000 in donations, earmarked for an independence referendum, had been used.
On the sim cards, a source with knowledge of the probe told the Sunday Mail: “They want to know the numbers connected with these cards which could also contain numbers called and text messages.”
“It’s not uncommon for people to have unregistered mobile sim cards which can be bought from any shop, there’s nothing wrong with having a so-called burner phone but police want a record of these phones in the SNP.”
Another source said there was an “extensive list” of items cops are interested in obtaining – including pens, pots and pans, jewellery and a fridge freezer.
Despite unanswered questions about the party’s finances, depute leader Keir Brown described the SNP as the “most transparent party” on Sunday. “We are the most transparent, most successful party … in Scotland,” the senior SNP figure told BBC Scotland’s Sunday Show.
“We have to increase that transparency. It is my ambition – and I know that it’s Humza [Yousaf]’s – to make sure that we are the most transparent party in Scotland and that we set the standard for transparency and shame other parties.”
Scottish Tory chairman Craig Hoy appeared on the programme after Mr Brown as he called the remarks “bizarre” and claimed the SNP was “addicted to secrecy”.
In an earlier interview with Sky News, Mr Brown admitted that he had not been notified until recently that party auditors resigned.
SNP leader Humza Yousaf only learned of the revelation on auditors after he replaced Ms Sturgeon in the top job – despite the auditors stepping aside in around October.
Earlier this week a senior SNP figure told The Independent it was likely that Ms Sturgeon would also be interviewed under caution, given that she is one of the three names believed to be on party accounts.
Some of the party’s MPs and MSPs have also said it is “inevitable” that Ms Sturgeon will be questioned by police under caution in the weeks ahead.
An SNP spokesperson said: “We have no comment on a live police investigation.” The Independent has approached Police Scotland for comment.