It was reported that officers are considering whether to quiz the party chief Peter Murrell over a donation from the pair, who won £161 million in the EuroMillions lottery.
The Weirs are said to have made a donation to a fund for a new independence referendum, only for Mr Weir to complain to the party and demand his money back, prior to his death in December 2019.
A police investigation was launched earlier this year after party members raised concerns about the whereabouts of £600,000 raised to fund a new independence referendum.
A Police Scotland spokesperson said: "We continue to assess a complaint of alleged financial irregularity.
“During this initial work further information has been received, which also requires to be assessed to determine if an investigation is required."
It is understood that Mrs Weir is not one of those to have made formal complaints. The matter was reported to Police Scotland in April.
A source told The Scottish Mail on Sunday officers were now looking through emails sent to Mr Murrell, who is the husband of Nicola Sturgeon.
They said: “Police officers have been looking at emails from Mr Murrell to various donors, including Mr and Mrs Weir.
“He was writing to these people seeking donations as part of a fundraising effort for a second independence referendum.
“But they then spent the money on other things. Some of the donors are now complaining that they were misled.
“From the party accounts, police can see the money was spent on other party business.
“There is no evidence emerging of personal benefit to Mr Murrell or anyone else.”
The Weirs won their then-record jackpot in 2011 and subsequently made several donations to the SNP adding up to millions of pounds.
Labour’s shadow Scottish secretary Ian Murray said: “This is an astonishing revelation which raises more serious questions about how the party of government is being run.
“For months questions have been asked about the state of the SNP’s finances.
“The police investigation must run its course, but, regardless of its conclusion, Mr Murrell must come clean and explain what is going on behind the scenes and explain what happened to this money, or he risks eroding trust in our entire political system.”
Scottish Conservative chief whip Stephen Kerr said: “The murkiness surrounding the allegations of missing funds within the SNP’s accounts is only continuing to grow.
“We have seen senior SNP politicians resign from their national executive due to the complete lack of transparency surrounding this situation.
Even their now former treasurer couldn’t get his party to open up their books. It is time the SNP cleared this up.
“As we focus on rebuilding from the pandemic, the last thing the country needs is the ruling party at war with each other over alleged missing funds from their party accounts.”
The SNP did not reply to requests for comment.
The Scotsman reported earlier this month the SNP’s problems around the allegedly missing £600,000 in donations would not have been helped by a decision made in 2014 to shut its books.