Carter, who won gold in the Chinese capital along with Michael Frater, Asafa Powell and global superstar Usain Bolt in a world record time of 37.10sec, was one of 32 athletes to test positive following the retesting of samples using new methods.
According to the Jamaican Gleaner, the 30-year-old failed for banned stimulant methylhexanamine.
Both Reuters and the Jamaican Gleaner are now reporting that his B-sample also tested positive.
This presumably means he will be disqualified from Rio 2016 and the team will lose their gold medal.
If this does happen, Caribbean neighbours Trinidad and Tobago would be promoted to the gold, Japan to the silver and Brazil to the bronze.
Carter, one of Jamaica's most successful sprinters, also won relay gold at the London 2012 Games and at three separate editions of the World Championships.
The International Olympic Committee are already re-testing all London 2012 samples submitted by athletes who failed in Beijing.
The case is slightly complicated, however, because Methylhexaneamine was only added by name to the WADA banned list in 2010, although it was indirectly banned before then.
"Methylhexaneamine is a stimulant developed in the 1940s and according to the Prohibited List, all stimulants are prohibited in competition (Section S6)" a WADA spokesman told insidethegames.
"It was always a prohibited substance, under a catch all category, but was added by name from 2010 onwards."
Carter should therefore also face a backdated ban of two-years, the maximum sanction for the offence at the time of the WADA rules, although some past Methylhexaneamine cases have resulted in a warning rather than a ban.
Neither Carter nor his agent, Adrian Laidlaw has commented on the reports.
The Jamaican Olympic Association confirmed an unnamed athlete from the country had failed at Beijing 2008.
Bolt, who boasts six Olympic gold medals, is hoping to seal a "triple triple" of 100m, 200m and 4x100m titles in Rio but the loss of any relay title would render this ambition impossible.