Agassi reveals in an upcoming autobiography that he used the recreational stimulant crystal meth in 1997 and avoided a doping suspension for a positive test by claiming he ingested the drug by accident in a spiked drink.
Under today's anti-doping rules, a player could face a ban of up to two years for use of the drug.
World Anti-Doping Agency president John Fahey said the body can't take any action against Agassi because of its eight-year statute of limitations, and that it's "unlikely" the ATP will either.
"WADA would, however, expect the ATP, which administered its own anti-doping program at that time, to shed light on this allegation," Fahey said in a statement.
International Tennis Federation president Francesco Ricci Bitti said he was "surprised and disappointed" by Agassi's disclosures.
"Such comments in no way reflect the fact that the Tennis Anti-Doping Program is currently regarded as one of the most rigorous and comprehensive anti-doping program in sport," he said.
Ricci Bitti said the incident occurred before WADA was founded in 1999 and when drug-testing was handled by individual governing bodies. The ITF assumed responsibility for the ATP's anti-doping program in 2006 and for the WTA Tour in 2007.
"The ITF, Grand Slams, ATP and Sony Ericsson WTA Tour are now unified in their efforts to keep tennis free of drug use, and this should not be overshadowed by an incident that took place over 12 years ago," Ricci Bitti said. "The statements by Mr. Agassi do, however, provide confirmation that a tough anti-doping program is needed."
The ATP said an independent panel makes the final decision on a doping violation.
"The ATP has always followed this rule, and no executive at the ATP has therefore had the authority or ability to decide the outcome of an anti-doping matter," the statement said.
Agassi writes in his autobiography "Open" that he was introduced to crystal meth by his assistant "Slim" at a time when his form was falling and he was having doubts about his impending marriage to actress Brooke Shields.
In excerpts from the book published in The Times of London, Agassi said he was informed by the ATP later that year that he had tested positive for the drug and could face a three-month ban for use of a recreational substance. He said he sent a letter to the ATP tour claiming he accidentally drank from a soda spiked with meth by "Slim" and asking for leniency.
Agassi said the ATP reviewed the case, accepted his explanation and threw it out.
Agassi, who married tennis star Steffi Graf eight years ago and has two children, retired in 2006.
"We would hope that Andre Agassi might now see his way to be a role model and alert youth and tennis players to the dangers of drug use and doping," Fahey said.
The Australian official said the case shows the importance of having a monitoring body like WADA in place to review and follow up on positive cases.
"This ensures that no doping case is swept under the carpet," Fahey said. "The anti-doping system under the World Anti-Doping Code now ensures that a hearing by an independent tribunal occurs and excuses cannot be acted upon outside of such transparency."
Methamphetamine is classified as a stimulant under WADA's list of banned substances. Although tennis rules at the time might have warranted a three-month ban, WADA's current guidelines on methamphetamine provide for a sanction of up to two years if an athlete cannot prove mitigating circumstances.
"We're stuck by our eight-year limitation rule, so we can't do anything," WADA director general David Howman told The Associated Press in Paris. "It will rest with ATP or perhaps ITF depending on how they've organized they're jurisdictional things. But 12 years back you start to say, 'For what, anti-doping?' It's a no-go because of the statute of limitations."
"I mean, at the end of the day he's confessed," Howman added. "He obviously hasn't been able to sleep in bed straight and he's come out and made a confession and you have to applaud that to a degree."