Mr Grady, the SNP’s chief whip in Westminster, stepped down from the role last week while claims that he “inappropriately touched” a male staffer in 2016 are investigated.
Yesterday, the Sunday Post reported that former First Minister Alex Salmond warned Nicola Sturgeon about Mr Grady’s alleged conduct more than three years ago.
But the Deputy First Minister told the BBC’s Good Morning Scotland that he was only told of the claims when they were reported last week.
He told GMS that the allegations “are being explored and examined and investigated” by the SNP, but could not say when any findings would be made public.
Mr Swinney also said he did not know when the party’s year-long investigation into Derek Mackay would finally conclude.
The former Finance Secretary has not appeared in Holyrood or held a surgery for constituents since his resignation in February last year.
Mr Swinney told GMS: “I can’t share those details with you because I don’t hold an office in the Scottish National Party, so I’m not close to these decisions within the party.
He added that the investigation’s findings would be communicated “as soon as it’s possible to do so”.
The Deputy First Minister also insisted that the party “has no locus” to intervene in the row over Mr Mackay’s continued acceptance of an MSP’s salary.
Mr Swinney told the BBC’s Good Morning Scotland that Mr Mackay’s continued membership of the Scottish Parliament was a “matter Derek Mackay to determine and to resolve”.