Peterson won their first bout in Washington in December by a score of 113-112 on two judges' scorecards while the other had Khan a 115-110 winner.
After the fight, the British boxer - who won an Olympic silver as a 17-year-old in 2004 - claimed a "home-town decision" had robbed him of victory.
Both Khan and Peterson had agreed to random testing by the Voluntary Anti-Doping Association (VADA) before the rematch.
Peterson's publicist, Andre Johnson, told RingTV.com this week that the boxer's camp was mystified by the test results. "We have tremendous respect for VADA and its mission.
"Lamont, Barry and the entire team emphatically support random drug testing in the most comprehensive manner possible," he said.
"We are working expeditiously with a team of pathologists and other medical specialists to confirm the origin of the test result and in full compliance with the rules of the Nevada State Athletic Commission.
"Lamont has never had a positive test either before or after this isolated occurrence."