The attorney general is visiting Israel to seek evidence as he considers bringing charges against two Israeli soldiers who killed two Britons.
Mr Hurndall was moving children away when he was shot
James Miller, 34, a Devon film-maker and Tom Hurndall, 22, a London peace activist, were shot dead in separate incidents by soldiers in Gaza in 2003.
Relatives of the men have asked Lord Goldsmith QC to prosecute for war crimes under the Geneva Convention.
During his trip he will meet Israeli ministers and military officials.
Israeli military prosecutors have insisted that further prosecutions will only take place if fresh evidence emerges.
But Lord Goldsmith said he believed the Israeli authorities would give him their full cooperation.
He said while in Israel he would be considering "whether there ought to be prosecutions here in either of these cases".
"I will carefully consider this without any preconceptions," he said.
"This is not about raising expectations about whether anything is going to happen one way or another."
Lord Goldsmith is hoping to meet Israeli Attorney General Meni Mazuz, Minister of Defence Amir Peretz and Minister of Justice Haim Ramon.
He is also seeking an appointment with the country's military advocate general, Brigadier Avichai Mendelblitt.
Mr Hurndall was moving children away from the army in the Palestinian town of Rafah when he was shot in April 2003.
Mr Miller was gunned down only a mile away three weeks later as he was making a film about Palestinian children.
No one has been prosecuted over Mr Miller's death
Israeli Defence Force (IDF) soldier Sergeant Taysir Hayb is serving an eight-year sentence for the manslaughter of Mr Hurndall but so far no one has been convicted of shooting Mr Miller.
Last month an inquest jury in London decided Mr Miller's shooting was unlawful and that the father-of-two had been murdered.
During the inquest Mr Miller's widow Sophy named the soldier who shot her husband as First Lieutenant Heib, from the Bedouin Desert Reconnaissance Battalion.
It was said he had been due to face a disciplinary hearing, but was acquitted by the head of the army's Southern Command.
Mrs Miller has requested for all the evidence from the military police investigation to be released.