Thuram, who ran out of contract with Barcelona, was supposed to announce his move to the French Ligue1 side on Friday as he revealed the problem.
The 36-year-old admitted that the problem had its effect on his family, as he indicated that his future remains unclear.
"Unfortunately, if I am holding this conference today it is not to announce my contract with Paris Saint-Germain, but to tell you the doctors discovered a congenital heart defect.
"It seems to be the same illness that my brother had a few years ago and it cost him his life on a basketball court.
"When I was a youngster playing for Monaco they told me I had something, but was fit to play.
"Things have evolved and today I am at risk. Yesterday the cardiologist found a malformation. We preferred to order more in-depth tests and we’ll have the definitive results within a month."
Juve Shock
In the wake of the problem, the medical staff of Juventus, where Thuram played for five seasons before joining Barca in 2006, were shocked by the news.
"Juventus never spotted anything,” said Juve doctor Riccardo Agricola.
"Thuram was always clear to play according to our tests. It is possible the signs of this malformation only manifested themselves after he left Juve."
Thuram, who played142 times for France, announced his international retirement after Les Bleus poor EURO 2008 campaign.
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