Investigators are working to verify Abrini's claims, the source told CNN.
Also, a computer used by Brussels attackers Ibrahim and Khalid El Bakraoui
and found in a garbage bin outside the group's bomb factory contained a file of research indicating La Defense shopping mall in Paris and a Catholic association were additional potential targets, the source said.
The Euro 2016 tournament
, slated to run from June 10 to July 10 in cities across France, is one of the biggest international sports spectacles in the world.
There were already fears about security at the championship. In November, the same cell carried out three suicide bombings outside the French national stadium while Germany was playing France. Eyewitness accounts obtained by CNN suggest the attackers tried but failed to get inside the stadium.
The computer the Bakraoui brothers used also had a 16-minute audio file in which one of the Brussels attackers is heard speaking to someone about future attacks against specific targets in France and Belgium, including when and where to carry them out, how many members of the cell should take part and how many should remain in reserve for future strikes, the source said. Investigators said the voice belonged to Najim Laachraoui, the cell's suspected bombmaker who blew himself up at the Brussels airport. The other person speaking with Laachraoui cannot be heard, but investigators suspect it was a senior ISIS operative in Syria, according to the source.
Abrini was one of six people detained in raids Friday across the Belgian capital. The Belgian federal prosecutor's office positively identified him as the third suspect in the March 22 Brussels Airport attack
-- the "man in the hat."
He also has been tied through surveillance video and DNA to the terror attacks in the French capital.
Investigators said the same ISIS network was behind the Paris attacks and the Brussels suicide bombings.
When the terrorists discovered the French were moving fast in their investigation
, they changed their plans, the Belgian prosecutor's office said.
"Eventually ... they urgently took the decision to strike in Brussels," the office said.
Police arrested Salah Abdeslam
, a key suspect in the Paris attacks, in Brussels on March 18. Four days later, suicide bombers struck at the Brussels Airport and subway station, killing 32 people.
In November, Paris prosecutor Francois Molins saidvestigators had learned Abdelhamid Abaaoud,
the ringleader behind the Paris attacks, had planned a suicide attack on La Defense.