Stewart Hosie and Angus MacNeil were reported to the Parliamentary Commissioner for Standards over claims they carried out their affairs with the reporter in hotels paid for by the taxpayer.
Kathryn Hudson, the Standards Commissioner, will not examine the claims because of the lack of any evidence or basis for an inquiry.
Shortly after news of his affair with Serena Cowdy broke, Mr Hosie announced he would stand down as deputy leader of the SNP in the autumn.
Mr MacNeil is alleged to have stayed with Ms Cowdy at the Park Plaza Hotel in London, where he has claimed for his bills in line with expenses rules.
Following the relationship with Mr MacNeil, Ms Cowdy is believed to have begun an affair with Mr Hosie, who recently split from his wife, the Scottish health secretary and SNP MSP Shona Robison.
The SNP dismissed the complaint to Ms Hudson by Conservative MSP Jackson Carlaw as a “political stunt”.
Accusing Mr Carlaw of hypocrisy given previous expenses scandals involving Tory MPs, the spokesman said the MSP was “playing politics with people’s private lives.”
A spokesman for the Scottish Conservatives said: “We respect the decision of the Standards Commissioner.
“Our view is it is right to question such cases to ensure that public funds are always used in support of parliamentary duties.”