The Sunday Times reported an alleged dispute between doping testers and the swimmer last year which the newspaper said had resulted in damage to a sample.
China's swimming association (CSA) said an investigation by world swimming body FINA had found the swimmer committed no anti-doping rule violation.
The CSA said Sun had rejected an out-of-competition doping test at his home in China on Sept. 4 last year over what the athlete said was a lack of proof of identification by the testers.
"After FINA called up an investigation of the issue, CSA ordered Sun Yang to fully cooperate with FINA and truly report every detail of the affair," the CSA said in a statement to state-run news agency Xinhua.
"According to the final decision of the FINA Doping Panel, FINA confirms the athlete did not commit an anti-doping rule violation."
FINA could not be immediately reached for comment, while the World Anti-Doping Agency said it was looking into the matter.
"I can confirm that WADA is aware of this case and that we are following up accordingly," Maggie Durand, WADA's manager of media relations and communications said.
Sun, a triple Olympic gold medallist and world record holder, was banned in 2014 for three months after testing positive for the banned stimulant trimetazidine during the Chinese national championships.
His lawyer Zhang Qihuai has threatened legal action, saying the newspaper reported with "a malign intention" which "severely damaged Sun Yang's reputation and violated his privacy."
"We reserve the right to file a lawsuit against the relevant international media which reported the incident," Zhang said in a statement to Xinhua.
(Reporting by Karolos Grohmann; Editing by Andrew Cawthorne and Alexander Smith)
