The Scottish Conservatives leader had referred himself to the parliamentary standards watchdog after reportedly failing to fully record his MSP salary, as well as almost £7,000 in outside earnings as a football referee.
The Commissioner is not releasing details of the allegations facing them.
Speaking last month, Mr Ross said: "This was an error on my behalf that shouldn't have happened and I apologise for not registering these payments on time.
"Since realising my mistake last week, I contacted the Office of the Register of Interests and made them aware of the situation. All payments have now been declared, including those from my MSP salary that are donated to charities."
The SNP’s Westminster depute leader Kirsten Oswal claimed Mr Ross was “the latest in a long line of Tories who find themselves up to their neck in sleaze”.
She continued: "By failing to declare thousands of pounds from multiple side hustles, and missing crucial votes in Parliament to run the line at football matches, Mr Ross is in clear breach of the rules.
“The irony, of course, is that it was Mr Ross who was first off the mark to demand that others resign for rule-breaking, even when that was disproven, but has now become strangely reluctant to follow his own advice.
“It is clear that, just like every other Tory, Mr Ross believes it is one rule for him and another for everyone else.”
A Scottish Tory spokesman said: “Douglas referred himself to the Standards Commissioner for investigation and he will support the conclusion they reach.”
Labour's shadow Commons leader Thangam Debbonaire has previously called for the watchdog to investigate claims Mr Rees-Mogg failed to declare £6 million in loans from one of his companies.
She said: "It is right that the Standards Commissioner is investigating what appears to be yet another egregious breach of the rules, with Jacob Rees-Mogg failing to declare millions of pounds of directors' loans.”
Mr Rees-Mogg has insisted the loans had been properly declared.