The man was found in the city of Jaffa in northern Israel on Friday morning, the newspaper writes.
He is said to have hidden near a mosque and been killed in a firefight with the police anti-terrorism unit and the security service Shin Bet.
The man has been identified as a 29-year-old man from the area around Jenin in the West Bank.
The attack took place shortly after 9 pm at a bar on Dizengoff Street in Tel Aviv, a popular street with many bars and restaurants.
Two civilians, aged 27 and 28, were killed in the attack, according to police.
Four others are being treated in hospital for life-threatening injuries, while two have moderate injuries and nine minor injuries.
Tel Aviv's police chief stated last night that they suspect terrorist motives, but that they do not rule out other motives.
"As far as we know, there are signs that this was terror," said Police Chief Ami Eshed.