Whyte landed the WBC interim heavyweight title with a unanimous-decision win over Rivas in London on Saturday.
But Boxing Scene reported on Wednesday that Whyte had "tested positive for one or more banned substances" prior to the fight, which was allowed to proceed by the British Boxing Board of Control (BBBofC).
Whyte's promoter, Matchroom's Eddie Hearn, said in a short Twitter statement that Whyte was cleared to fight following "extensive" testing before the bout by the Voluntary Anti-Doping Association (VADA) and UK Anti-Doping (UKAD).
Hearn did not say whether the 31-year-old had tested positive. Omnisport has asked the BBBofC and UKAD for comment.
There has been no public indication of what banned substance may have been detected.
Whyte, who served a two-year ban from October 2012 after failing a doping test, could face a fight to save his career if he is shown to have committed a further offence.
The WBC said it had not been privy to any details of a failed test.
The organisation said in a statement released on Thursday: "The WBC has not received any notification from anyone about a positive anti-doping test allegedly yielded by Dillian Whyte in connection with last Saturday’s fight against Oscar Rivas for the WBC interim heavyweight championship.
"The WBC has requested that the BBBofC, as the local, governing entity that oversaw that fight, formally provide any available information to the WBC.
"The fight's promoters contracted the Voluntary Anti-Doping Association (VADA) to perform pre-fight and after-the-fight anti-doping tests on both fighters.
"The WBC is not aware that any of the test’s results VADA has received up to now have yielded any adverse findings.
"The WBC created the Clean Boxing Programme which is administered by VADA, and which is a top priority of our organisation.
"The WBC will not make any comments about the situation at hand until it receives the proper, formal communication from the BBBofC."
Whyte secured a dominant win over Rivas, with two judges scoring it 115-112 in his favour and a third 116-111.
Though they made no reference to Whyte's case, the BBBofC released a statement on Thursday titled 'British Boxing Board of Control anti-doping regulations'.
It read: "With regard to the above, United Kingdom Anti-Doping undertake all anti-doping procedures on behalf of the British Boxing Board of Control and any subsequent findings, decisions, suspensions and sanctions are upheld by the British Boxing Board of Control in line with United Kingdom Anti-Doping.
"No further comment will be made at this time."
Photo Getty Images: Dillian Whyte and Oscar Rivas