Craig is the Republican senator who pleaded guilty to misdemeanor disorderly conduct charges earlier this year after his arrest in a Minneapolis airport bathroom for propositioning an undercover police officer.
Mike Jones of Denver appeared on a Palm Springs, California radio show Wednesday night.
Jones was promoting his book on the Haggard affair on the "Bulldog Bill Feingold Show" broadcast on KNWQ-AM when the show went into a commercial break.
It was during that commercial break Wednesday night that Jones made an accusation that Craig had visited him in Denver in February 2005.
A TV news photographer for KESQ-TV, the ABC affiliate in Palm Springs, kept recording as Jones talked about his contact with Craig.
Feingold reportedly asked Jones if Craig met him in a hotel room.
Jones responded, "No, he came to see me."
Jones did not reveal if he had sexual contact with Craig.
Craig's office told KESQ-TV, "Mike Jones' allegations are completely false."
The Palm Springs TV station also reports that Craig's office added, "Clearly anyone can make an accusation absent of details that would be easy to refute."
Craig announced this week he will remain in the Senate after agreeing to resign at the end of September after news of his arrest broke in the media.
A Minnesota judge ruled Thursday Craig could not withdraw his guilty plea.
Mike Jones told 9NEWS "no comment" when reached Friday night.
Haggard resigned from the New Life Church he founded and as leader of the National Association of Evangelicals in November of 2006 after Jones made allegations Haggard paid him for sex and used methamphetamine with the Denver escort.
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