Malaysia's Sports Minister Khairy Jamaluddin said on Tuesday that an athlete from the country had tested positive for a banned substance.
He declined to name the person because further tests were ongoing.
But a Malaysian newspaper reported on its website that it was Lee and that he had failed a random test at the World Badminton Championships in Copenhagen in late August.
The Badminton World Federation declined to comment, saying its anti-doping regulations required confidentiality, while the Badminton Association of Malaysia and other sports officials could not immediately be reached for comment.
Lee, 31, is a national icon in the Southeast Asian nation and has consistently topped the badminton rankings, despite having failed to win a world or Olympic title.
Malaysians took to social media to express their disbelief, and support for Lee.
"There must be a reason. We have to lend him all our support Malaysian!" one user wrote on Twitter.
Khairy said in a statement that the country's anti-doping agency was informed in a letter from the international sports federation on October 1 of the failed doping test in an international tournament.
He added that the athlete had submitted another sample for further tests, the results of which were still pending. He gave no indication of when the final results would be known.
Khairy said he had asked top sports officials to undertake "a thorough investigation" of all the medical treatment that Lee had received.
If the results come back positive, it would mark Malaysia's second doping scandal in recent months.
Earlier this month, the head of the Wushu Federation of Malaysia resigned to take responsibility after Asian Games champion Tai Cheau Xuen tested positive for doping and was stripped of her gold medal.
In Copenhagen, Lee lost to China's Chen Long in the final.

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