Police say they have now confirmed the driver's identity, but would not reveal his name, reports BBC.
But Catalan official Joaquim Forn told local radio: "Everything suggests the van driver is Younes Abouyaaqoub".
Authorities say they cannot rule out the possibility that he has slipped across the border to France.
Islamic State has claimed responsibility for the attack, in which a van travelling at high-speed drove through crowds of tourists and local people walking along Las Ramblas, leaving a trail of dead and 120 injured from 34 countries; according to Reuters.