They weren't able to arrest Zaghba, who was traveling on an Italian passport, as having extremist material on a phone isn't against the law in Italy.
Italian media reported that officials suspected he was bound for Syria and that Italian authorities had alerted their British counterparts about his movements.
Police say Zaghba, 22, was one of three men who rammed a van into pedestrians on London Bridge before launching a stabbing spree in bars and restaurants at nearby Borough Market on Saturday night. All three were shot dead by police in the attack.
Zaghba's reported Syria travel plans raise further questions about whether British authorities could have done more to prevent the attack.
London's Metropolitan Police Service said Zaghba was not a "person of interest" before Saturday's attack.
Earlier, London police admitted that one of the other two attackers, Khuram Shazad Butt, was on their radar as a member of the outlawed radical Islamist group al-Muhajiroun, co-founded by notorious hate preacher Anjem Choudary. He appeared in a 2016 television documentary called "The Jihadis Next Door."