The Chinese freestyler was originally suspended for eight years by the World Anti-Doping Agency (WADA) in 2020 for smashing vials of blood during a 2018 test, the circumstances of which he still disputes.
The ban was reduced on appeal to four years and three months by the Court of Arbitration for Sport in 2021.
"I hope that I'll be able to pick a competition and return to the starting block as soon as possible," the 32-year-old said in an interview published by state-run media outlet The Paper.
Sun's return comes with China's swimmers under intense scrutiny since it emerged that WADA allowed 23 of them to compete at the 2021 Tokyo Olympics, despite testing positive for a banned substance.
WADA accepted China's explanation that the swimmers unwittingly consumed the substance through food at their hotel.
'No big deal'
Sun's return is too late for him to compete at this summer's Paris Olympics, but he hinted that he was setting his sights on longer-term goals.
"The Olympics are just a competition for me, they will end, and after they end, there will be another one," Sun said.
"I am frequently doing some simulated competition tests now that I've returned to training... I am constantly trying to recapture that feeling," he said.
The two-metre tall (6ft 7in) Sun was the first Chinese swimmer to win Olympic gold, in 400m and 1500m at the 2012 London Games, but has long been a controversial figure in the pool.
Some rivals called him a cheat at the 2016 Rio Olympics and two competitors refused to stand with him on medal podiums at the 2019 world championships.
Sun was also given a three-month ban in 2014 after testing positive for a banned substance.
"I think compared to other athletes I am very lucky, and I am very grateful and thankful," Sun said, referring to his past achievements which also include 11 world championship golds from 2011 to 2019.
He said he had felt "very dark" when he initially found out about his second ban, but that his time away from the pool had given him the space to develop other interests.
"When I look back (on the past four years), I think it's really no big deal," Sun said.
"In fact, the biggest change in my past four years is that I started a family and now have another half," he said, referring to his marriage to gymnast Zhang Doudou.
"These four years have added some colour to my life."