Sources familiar with truce talks have told the BBC that Israel has informed Egyptian mediators it will agree to end military action.
There has been no official confirmation of this from Israel where PM Benjamin Netanyahu is meeting his security cabinet.
Both sides are facing international pressure to end hostilities.
The Israeli security cabinet will vote on a proposed unilateral ceasefire that would take effect within 24 hours, Israel's public broadcaster Kan reported.
Earlier a senior Hamas official said he expected a ceasefire deal with Israel in "a day or two", while Mr Netanyahu on Wednesday vowed to continue the military operation until "calm and security are restored".
On Thursday more than 100 Israeli air strikes targeted Hamas infrastructure in the north of Gaza. Hamas retaliated with rocket fire.
Fighting began in Gaza on 10 May after weeks of rising Israeli-Palestinian tension in occupied East Jerusalem that culminated in clashes at a holy site revered by both Muslims and Jews. Hamas began firing rockets after warning Israel to withdraw from the site, triggering retaliatory air strikes.
At least 232 people, including more than 100 women and children, have been killed in Gaza so far, according to its Hamas-controlled health ministry. Israel has said at least 150 militants are among those killed in Gaza. Hamas does not give casualty figures for fighters.
In Israel 12 people, including two children, have been killed, its medical service says. Israel says some 4,000 rockets have been fired towards its territory by militants in Gaza.
People involved in the discussions with the two sides also told the Wall Street Journal that a ceasefire could come as early as Friday. Egyptian officials have made headway in negotiations with Hamas's leadership, and the Israeli military has privately conceded that it is nearing the completion of its objectives, US and foreign officials are quoted as saying by the newspaper.
An Egyptian security source also told Reuters news agency the two sides had agreed in principle to a ceasefire after assistance from mediators but negotiations were still taking place.