CHARLOTTE, N.C. -- It is highly unlikely that AJ Allmendinger's positive test for amphetamines resulted from a single pill taken one time, as the suspended Sprint Cup driver recently stated, a source close to the situation told ESPN.com.

It also is highly unlikely that Allmendinger will complete NASCAR's Road to Recovery program, necessary for reinstatement, by the end of August, as the driver stated, the source said.

"That's not going to happen," the source said.

Allmendinger, who drove the No. 22 Penske Racing Dodge in Sprint Cup, was suspended indefinitely by NASCAR on July 24. He likely will need a lengthier recovery period, according to the source.

The driver said last week that the positive test resulted from prescription Adderall that he was given by the friend of a friend two days before he was randomly tested at Kentucky Speedway on June 29. Adderall is administered medically to control symptoms of attention deficit hyperactivity disorder.

However, the source told ESPN.com that Allmendinger's one-pill defense is not consistent with the test results.

Adderall can remain in a person's system for up to 72 hours, but the source said that in Allmendinger's case it was "very unlikely that one-pill usage one time would be detected after 24 hours."

Adderall does contain compounds of amphetamines, but so do other prescription and illegal drugs.

"They're all going to be on their banned list," said Dr. Don Catlin, co-founder and president of Anti-Doping Research & Support Clean Sport and founder and the former director of the UCLA Olympic Analytical Lab.

Catlin said that without knowing the dosage of the pill and the level of sensitivity in the laboratory testing he could not make an educated statement on whether one Adderall pill taken one time could produce a positive result. In general, Catlin said, Adderall would show in one's urine for a couple of days.

NASCAR officials have said they are unaware of the specific substance that Allmendinger ingested, other than it was an amphetamine. NASCAR has declined to comment beyond that.

NASCAR denied ESPN.com's request to interview Dr. David Black, who heads the Nashville-based Aegis Sciences Corp. that runs the drug-testing program for the sport, regarding Allmendinger's claims.

"We don't feel it's appropriate nor necessary at this time for NASCAR to discuss AJ Allmendinger's situation while he's undergoing the Road to Recovery program," NASCAR spokesman David Higdon said. "NASCAR's involvement remains as a facilitator between the program and AJ to provide him the necessary means to be considered for reinstatement."

Allmendinger, according to the source, also did not reveal to the medical review officer during standard questioning given before the random test that he took anything given to him by another person that possibly could register a positive test.

Such questions are common in other sports, with the Olympics' guidelines setting the standard.

"That should be the place where they disclose that on the intake form," Catlin said. "It's an opportunity for an athlete to say what they are doing and an opportunity to declare if they have a therapeutic use or exemption."

Allmendinger originally speculated while awaiting test results of the "B" sample split from his original sample that the positive test was triggered by a supplement or over-the-counter drug he might be taken.

Black, reached by ESPN.com last month, said this was unlikely.

"Certainly, if that had been a possibility (it) would have been ruled out before any action was taken,'' Black said. "On every positive test we have, we look to rule out the possibility of a supplement being involved.

"I'm not aware of any commercial products that would have influenced the test outcome.''

Allmendinger's reference to a prescription pill for Adderall wasn't mentioned until more than a month after he first was suspended.

Based on his experience with Olympic athletes, Catlin said it's not uncommon that they concoct stories to get a reduction in penalty for testing positive. The penalty for a positive test in the Olympics generally is a two-year ban from competition.

Catlin added it is Olympic policy to name the specific drug that was discovered in a test to avoid gray areas, such as the one in Allmendinger's situation.

"They just believe it's better to explain the program and facts and put out a lot of information than it is to put out information that can be read in a different way,'' Catlin said. "I certainly support that. It's a program I developed for them."

In most sports, amphetamines are considered a performance-enhancing drug because they increase aggression, confidence, alertness and concentration. Adderall is used by many who have been diagnosed with ADHD to help them concentrate on tasks. Others, according to a 2011 report in USA Today's college section, use the drug to get high.

Allmendinger said he does not use Adderall as a therapy for ADHD.

Dr. Charles Yesalis, emeritus professor at Penn State and an expert on performance-enhancing drugs in sports, said Adderall and other amphetamine-based products definitely would enhance a race car driver's performance.

"You're talking about a sport where a tenth of a second a lap difference is a big deal," he said. "It blows my mind the [drivers] that hit their mark every time. It's a no-brainer everybody would concede that in NASCAR concentration is unbelievably critical."

Because there hasn't been a specific case study on whether amphetamines might enhance a driver's performance, Catlin said advantages from the drug are purely speculative.

"I suppose if the drivers are looking to stay hyper-alert, that'll do it," Catlin said of the taking of amphetamines.

Yesalis said there is cause for skepticism when an athlete says he took a pill without fully knowing its contents.

"There's a lot of people that do it, but very few that are subject to drug testing," he said. "If you are a drug-tested athlete, you should be darn paranoid about it."

In his interview last week with ESPN.com, Allmendinger insisted he simply used "bad judgment."

"Unfortunately, I hadn't been sleeping very well all year, just putting all the pressure I did on myself," he said. "It was just bad judgment. People are going to write it was stupid on my part, and I agree with them."