Italy's main newspapers named the suspect as Youssef Zaghba, 22, the son of an Italian mother, from Bologna, and a Moroccan father, who had passports from both countries.
British police have confirmed the identity of two of the three attackers but had been retaining the name of the third while investigations into possible accomplices and contacts continued.
The Italian reports said Zaghba was intercepted at Bologna airport last year as he was about to board a plane for Turkey, with the apparent intention of joining ISIS terrorists fighting in Syria.
According to the reports, Zaghba's status as a potential terrorist was notified to the British and Moroccan secret services.
A London police spokesman said: "We haven't released anything at the moment, nor are we confirming anything but as soon as we are ready to name him, it will be on our website. We're hoping to get that out soon."