Sun was banned by the Switzerland-based Court of Arbitration for Sport (CAS) in March after the World Anti-Doping Agency (WADA) appealed against a decision to clear him of wrongdoing during a 2018 doping test.
Swimming World said the three-times Olympic champion's appeal had been registered by the Swiss federal court on April 29.
Reuters was unable to confirm with the court.
Sun, who was given a three-month ban for doping in 2014, said in March that he had retained a lawyer to appeal to the Swiss federal court.
The 28-year-old is the reigning world and Olympic champion in 200 metres freestyle and won two gold medals at the 2012 London Games and another at Rio de Janeiro in 2016.