Khattab was convicted and sentenced in May 2016 for helping to recruit jihadists for Syria.
Khaled Khattab, a friend of airport attacker Najim Laachraoui, was convicted and sentenced in May 2016 for helping to recruit jihadists for Syria, a prosecutors' spokesman said.
But the 26-year-old Khattab was allowed to go free while he was awaiting a further hearing to finalise the details of his jail term, and was arrested in Turkey.
"Apparently he fled for Syria and the Turks arrested him. We are asking for his extradition," spokesman Eric Van Der Sypt told AFP, confirming a report in La Derniere Heure newspaper.
"During the hearing we asked for his immediate arrest," Van Der Sypt said. "The court did not take us up on it and that is their right."
Khattab, a dual Belgian-Syrian national, received the harshest of 26 sentences in a mass terror trial of people linked to top Belgian jihadist recruiter Khalid Zerkani.
Khattab had been arrested in Belgium in October 2014 after having returned from a visit to Syria, La Derniere Heure reported.
But he was allowed his freedom during the subsequent trial as he had a home in Belgium.
La Derniere Heure said the court had nonetheless noted Khattab's "worrying frame of mind" after a CD glorifying the Islamic State group was found in his police cell during his initial detention.
Bomber Laachraoui, 24, was also convicted at the same trial and sentenced to five years in jail in absentia.
Laachraoui was one of two suicide bombers who struck Brussels airport on March 22 last year, while a third blew himself up on a metro train, killing 32 people in all.
Investigators also believe Laachraoui was a bomb-maker for the November 2015 Paris attacks and that the same Brussels-based cell was responsible for both incidents, which were claimed by the Islamic State.
Belgium, a country divided along linguistic and political lines, has been accused of multiple failings in keeping track of home-grown extremists in the wake of the Paris and Brussels attacks.
In one revelation, Turkey said Belgium ignored warnings from Ankara after it deported Ibrahim El Bakraoui, the second airport bomber, to the Netherlands as a "terrorist fighter" in 2015 following his arrest near the Syrian border.