Sources cited in Belgian media say Abrini is also likely to be the "man in the hat" seen on CCTV before the blasts in the Brussels airport departure hall on March 22, according to BBC News.
Prosecutors confirmed that several arrests had been made in connection with the Brussels attacks.
The attacks on the airport and a metro station left 32 dead.
The gun and bomb attacks in Paris on November 13 killed 130 people.
Read alsoRussian propaganda: Brussels Attacks "Europe's fault. Or maybe staged"Although the Belgian prosecutors confirmed some arrests, they would give no further details.
Local media reports suggest that Abrini was arrested in the Anderlecht district of Brussels.
Read alsoBelgian intelligence had precise warning airport targeted for bombing – mediaSome media say that one of the other men arrested is suspected of helping suicide bomber Khalid el-Bakraoui at the Maelbeek metro station, but this has not been confirmed.
Belgian authorities had on Thursday released new video footage of the "man in the hat", appealing for the public's help in finding him.
Abrini, 31, is believed to have been filmed at a petrol station with Salah Abdeslam, another arrested Paris attacks suspect, two days before the attacks there.
Abdeslam was detained in Brussels in March, days before militants launched attacks in the Belgian capital.
