Details were leaked to the press by a party staffer unhappy at the decision to oust David Duguid as a candidate at the election and select Mr Ross as his replacement.
Mr Ross has insisted he has “no issue” with his expenses being scrutinised.
READ MORE: Ross has ‘serious’ questions to answer over travel expense claims
Only travel from an MP’s declared home airport – Inverness or Aberdeen for Mr Ross – can be claimed as constituency travel.
Any other travel must be classed as a “diverted journey” and MPs must provide detailed notes alongside every claim to explain why it was diverted.
Some of the dozens of cases identified by Mr Ross’s team in November 2021 include £58 parking at Inverness airport in July 2018 while parliament was in recess and £43 rail travel from Heathrow to central London the day after Ross refereed a match in Iceland.
In October 2019, he claimed for a flight from London to Glasgow and for £109 parking with NCP car parks.
On November 1, 2020, he claimed £48.99 for parking the day he refereed a Celtic game.
A senior Tory source told the paper his team discussed the travel claims when contacted by journalists but hoped nobody would pick them up.
The Sunday Mail said they had seen messages from November 2021 which saw Mr Ross’s closest aides refer to them as “dodgy” and suggest they “bluff ” it out.
The leak to the press comes after Mr Ross replaced ousted David Duguid as the candidate in the new Aberdeenshire North and Moray East constituency.
On Wednesday night, the party’s Management Board stopped the former Scottish Office minister from contesting the new seat as they claimed he was too ill.
Mr Ross then announced his intention to “lead from the front” and stand instead.
However, Mr Duguid has insisted that the party’s claims he is “unable to stand” due to ill health are “simply incorrect”.
A party insider said: “The latest antics from Douglas are a disgrace and he should be ashamed of himself.
“He has always wanted to stay at Westminster and he’s completely screwed over a hard-working colleague to get there. Many of us are disgusted with it.”
Speaking to journalists on the campaign trail in Paisley, John Swinney said there were serious questions to answer.
The SNP leader said: “The report in the Sunday Mail this morning about Douglas Ross allegedly using public funds to support his career as a football linesman raises very significant issues and I think Douglas Ross has got to set out all of the information about this particular issue.
“I’m not going to jump to conclusions about people. I don’t know the details about this, but (this) raises very, very significant concerns.
“Douglas Ross is normally the first to be out of the stables demanding that everybody sets out all of the information, so I think Mr Ross should do that right away because the story raises very significant and serious issues of the potential misuse of public funds.”
READ MORE: Swinney: SNP will work with Labour government
Mr Ross said: “I have only ever claimed expenses related to my role as a member of parliament and the costs of getting me to and from Westminster. “These have all been agreed by IPSA, the independent body that oversees MPs expenses, but I would have no issue with them being scrutinised again.”
