"Clearly, we are dealing with a large body of mainly young men, who have the potential to come back and have the potential or the intent and capability to carry out attacks we have seen in Paris in the last week," Wainwright was cited as saying by BBC in a meeting with the British Home Affairs Committee.
"We are talking about 3,000 to 5,000 EU nationals who are potentially a threat," he added.
According to the head of the EU law enforcement agency, European police face a security gap and lack "the necessary capability to fully protect society from these kinds of threats," being unable to monitor terrorist suspects' online communications.
Several European countries' authorities have expressed concern in recent months over their citizens traveling to the Middle East to fight alongside militant groups, such as the Islamic State (IS).
The gunmen behind last week's terror attacks against satirical magazine Charlie Hebdo, brothers Cherif and Said Kouachi, had reportedly trained alongside al-Qaeda in the Arabian Peninsula in Yemen, while kosher supermarket gunman Amedy Coulibaly appeared to pledge alliance to IS in a video that surfaced online, following the attacks.
