Mr Swinney led the SNP for almost four years, but stood down in June 2004 in the aftermath of disappointing European election results.
At the time he said internal backbiting within the party and criticism of his leadership was behind the decision.
He has now “unreservedly” ruled out returning to the post.
When asked if he would stand again for the leadership of the SNP, Mr Swinney told the Sunday Herald: “Unreservedly, absolutely in no circumstances, there is no way of you configuring any signal I am possibly giving you, to say anything other than ‘no’.”
He added that in 2004 he had come to the “very tough personal conclusion” that it was not in the interests of the party for him to continue as leader.
“I have certainly no intention of going back to that territory,” Mr Swinney stated
Current Deputy First Minister Nicola Sturgeon has already declared she would like to succeed Mr Salmond as first minister.
“Of course that is something I would like to think that one day I will get the chance to do,” she said in March.
When asked if Ms Sturgeon has what it takes to be first minister, Mr Swinney told the Sunday Herald: “Yes.”
When Mr Swinney stood down he said that the “constant and relentless speculation” over his leadership was obscuring “the political objectives of the SNP”.
He stated: “I have come to the view that the SNP cannot make the electoral progress I believe is possible if our vital political message is communicated through an endless debate about my leadership.’’
Mr Salmond replaced Mr Swinney as leader of the SNP, with Ms Sturgeon appointed his depute leader.
He said at the time a “huge number” of party members had urged him to stand again for the post, which he had previously held, despite him having declared: “If nominated, I’ll decline. If drafted, I’ll defer. And if elected, I’ll resign.’’