The PGA Tour refuted the claim.
"There is no truth whatsoever to these claims. We categorically deny these allegations," Ty Votaw, executive vice president of the PGA Tour, said in a statement.
Woods' manager Mark Steinberg also slammed Olsen's suggestion.
"These claims are absolutely, unequivocally and completely false," Steinberg said in a statement.
"They are unsourced, unverified and completely ridiculous."
Olsen has now backtracked completely.
"Everything I said on that radio interview was only my opinion and not based on any firsthand knowledge or facts," Olsen told ESPN.com.
A statement was posted on the radio station's website in which Olsen said: "I want to make a full retraction to everything I said for the entire radio interview, and I apologise to Tiger...(commissioner) Tim Finchem and the PGA Tour."
If Woods failed a test for performance-enhancing drugs, the PGA Tour has said it is required to announce a suspension. The ban would also be for more than a month.
If Woods failed a test for a recreational substance, the tour's policy is not to disclose any penalties.
Woods has not played since he withdrew from the Farmers Insurance Open at the start of February, less than a week after firing a career-worst round of 82 at the Phoenix Open.
-AAP