As authorities tried to establish Abdeslam's movements and whereabouts, a source said he travelled through Italy in August with a companion, but his presence caused no alarm because he was not a wanted man at the time.
His companion was Ahmet Dahmani, a Belgian man of Moroccan origin who was arrested in Turkey last week on suspicion of involvement in the Paris attacks, the investigative source said.
In Belgium, prosecutors said they had charged a fourth person with terrorist offences linked to the Paris attacks.
They released all 15 others detained in police raids on Sunday. Two of five people detained on Monday were also released while the other three had their custody prolonged.
Soldiers patrolled the streets of Brussels, which has been in lockdown since Saturday.
The metro, museums, most cinemas and many shops were shut on Monday in the usually bustling EU capital where many staff have opted to work from home. There was also no school or university for almost 300,000 students.
On the Grand Place, a historic central square that usually draws crowds of tourists, an armoured military vehicle was parked under an illuminated Christmas tree.
NATO, which raised its alert level after the Paris attacks, said its headquarters in the city were open, but some staff had been asked to work from home. EU institutions were also open with soldiers patrolling outside.
Interior Minister Jan Jambon told RTL radio, however, that the capital was still operating. "Apart from the closed metro and schools, life goes on in Brussels," he said.
City buses were running normally and many shops in the suburbs were open.
Workers were also setting up stalls for the city centre Christmas market, which is due to open on Friday, and organisers of the Davis Cup tennis final between Belgium and Britain in the city of Ghent, 55 km (35 miles) from the capital, said it would go ahead this weekend.