The retired sprint king, who turned 34 on Friday, is understood to have taken a test a few days ago which returned positive today.
The Jamaican is said to be have gone into self-isolation but, as reported by Nationwide Radio XJ, it is unclear if he has been displaying symptoms of the virus.
Bolt celebrated his 34th birthday with a surprise party and the report adds that Manchester City and England star Raheem Sterling was in attendance, APA reports citing The SUN.
Bayer Leverkusen winger Leon Bailey was also allegedly there.
Local media did express concern over Bolt's party amid reports over a lack of face masks although it is unclear if safety precautions were followed or not.
Jamaica has had a confirmed total of 1,413 Covid-19 cases and 16 deaths on the island of around 3million.
The athletics superstar enjoyed his first birthday as a father this year after he and long-time partner Kasi Bennett welcomed their baby girl Olympia Lightning in May.