Such a system would alert residents of incoming rocket attacks and allow them to take shelter, the Israeli daily Maariv reported Tuesday.
Home Front Commander Maj. Gen Yair Golan said the defense establishment intends to assess the situation in the coming days, and decide whether to install an early warning system in Israel's southernmost city, the newspaper said.
Hours after Monday's rocket attack in which a Jordanian citizen was killed and four others injured, Israeli security officials tracked down the remains of one of the rockets.
Israeli security officials said five rockets were fired in two salvos at Israel's southern city and the Jordanian resort of Aqaba.
Jordanian security officials Tuesday said they had concrete evidence the rockets were fired from Egypt's Sinai Peninsula. Israel Radio said the officials said the Hashemite Kingdom expects Egypt to prevent such attacks.
Meanwhile, Knesset member Shaul Mofaz, the former Israeli defense minister and chief of staff, told the radio it appears Hamas and Hezbollah elements were involved in the attacks, which he said have "an Iranian footprint."