Paris and Cairo are seeking a more formal ceasefire for "a year, 18 months if possible," a French official, speaking on condition of anonymity, said.
Israel announced a unilateral ceasefire on January 17 after a ground, air and naval assault on Gaza had left 1,330 Palestinians dead, more than one-third of them women and children.
Hamas declared its own cessation of hostilities against Israel a day later. At least 13 Israelis, three of them civilians, died during the war.
Israel's stated aim of the war on Gaza was to halt rocket fire by Palestinian fighters into Israeli territory.
Palestinians and human rights organisations said the Israeli attacks amounted to collective punishment of the Gazan population.
At least 40 rockets and mortar shells have been fired into Israel by Palestinian rocket squads since the unilateral ceasefires were declared.
Israel has in the meantime launched several air and artillery raids on Gaza.
Egypt has been in contact with both Israel and Hamas in an attempt to formulate a deal under which Hamas rocket attacks would cease in return for a lifting of Israel's protracted economic blockade of Gaza.
A bilateral truce could also include an undertaking by Hamas to free Gilad Shalit, an Israeli soldier captured in Gaza in June 2006.
Hamas expects Israel to agree to reporn crossing points into the Gaza Strip "within the next few days", a Hamas official said on Saturday.
Gaza's crossing points have been closed to all but essential supplies by Israel since June 2007, when Hamas, which Israel deems to be a "terrorist" organisation, pushed forces loyal to Mahmoud Abbas, the Palestinian president, from the territory.