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Wainwright told the newspaper that the Paris attacks last November showed that ISIS (also known as ISIL, the Islamic State and Daesh) had gained an international dimension and that further attacks were expected.
"Europe is currently facing its biggest terrorist threat in more than 10 years," Wainwright told NOZ.
Wainwright also warned about the high number of "international fighters," Europeans who have left to gather combat experience in a terrorist training camp abroad and then came back to Europe.
According to Europol, between 3000 and 5000 international fighters came back to Europe.
"The growing number of foreign fighters is presenting EU countries with completely new challenges," Wainwright told NOZ. Most of the perpetrators of the Paris attacks were European nationals who had travelled overseas and then come back to Europe to plan the attacks.
The Europol chief also mentioned that the stream of refugees coming into Europe from Syria does not necessarily increase the terrorist threat. "There is no concrete evidence that terrorists systematically use the stream of refugees to pass through to Europe undetected," Wainwright noted.
"It is to be expected that ISIS or other religious terrorist groups will carry out an attack somewhere in Europe - with the aim of killing as many civilians as possible."
Wainwright added that attacks were to be feared not only from groups, but that the threat of individual perpetrators was still very present. "In addition, there is a risk of individual terrorists, this has not been reduced," he said.
In an effort to combat the increasing terror threat in Europe, Europol opened the European Counter Terrorism Centre in January. The centre collects information from all over the continent and links European police together.