Fahey says only Usada can reopen Armstrong's case and there would have to be an "enormously powerful reason" for it to do so.
The Australian said: "He did what he did. He did not co-operate, did not defend the charges. He was dealt with by proper process and the reasoned decision released by Usada was irrefutable.
"It would take something close to a miracle to see it change in his case."
Armstrong said on Monday he would testify with "100% transparency and honesty" at any inquiry into doping by the UCI, cycling's governing body, as long as his punishment is the same as other guilty parties.
"If everyone gets the death penalty, then I'll take the death penalty," Armstrong told the BBC.
"If everyone gets a free pass, I'm happy to take a free pass. If everyone gets six months, then I'll take my six months."
Armstrong retired from cycling in 2011 after initially quitting in 2005.
Listen to the full interview with Lance Armstrong on BBC Radio 5 live from 21:30 GMT on Tuesday 12 November
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