If this is true, Abraham would be in violation of the program and subject to potential disciplinary action from the NFL.
Abraham is subject to random testing after being arrested for a DUI last year.
According to the New York Post story, Abraham passed a lie detector test set up by his agent, Tony Agnone, to prove his innocence.
The Jets and Abraham refuse to discuss the allegation with the media.
"I won't comment on it," said Jets coach Herman Edwards. "I can't comment on it."
"It's in the best interest of John (Abraham) not to comment," said a team spokesman. "He was going to say, 'no comment' anyway."
Since last year's arrest, Abraham has handled himself very well according to Edwards.
"He's been a model citizen," said Edwards. "He has done everything we've asked him to do. That is all I know."