Barak said he had discussed the plan with Tzipi Livni, the leader of Israel's Kadima party trying to form a coalition government, and that they were considering a response.
"There is definitely room to introduce a comprehensive Israeli plan to counter the Saudi plan that would be the basis for a discussion on overall regional peace," he told Israel's Army Radio.
Barak's announcement came as Livni sought a two-week extension to form political alliances in a new government, having failed to attract the ultra-orthodox Shas party to join Kadima and Barak's Labour party in the administration.
Livni was elected leader of Kadima last month, taking over from Ehud Olmert who resigned as prime minister in the wake of a corruption scandal but remains in office in a caretaker capacity until a new government is formed.
Livni has already won an initial agreement from Barak, the leader of the Labour party, to join a coalition under her leadership.
But her efforts to attract Shas, which is making a number of demands, have so far proved fruitless.
Al Jazeera's Sherine Tadros, reporting from Jerusalem, said the Shas party had a strong bargaining position.
The Shas party knows that Livni really needs it in order to become prime minister and form a strong government acceptable to the Israeli public, our correspondent said.
The religious Shas party, which has long billed itself as a party that represents Israel's poor, has been demanding increased government spending of about $270m on social welfare as a price for joining a Livni-led coalition.
Scramble for numbers
With Labour in her corner, Livni would control 48 of the 120 seats in parliament.
"She could go to the Knesset [to ratify a government] with the seats she already has, but she believes she can do it in the end," Gil Messing, a Livni spokesman, said.
Without Shas, she could form a minority government relying on precarious support from outside the coalition of left-wing and Arab parties wary of a national election that opinion polls show Benjamin Netanyahu's right-wing Likud would win.
Shas's membership would boost that number to 60, a wafer-thin coalition but enough to stop the opposition from toppling her government in no-confidence votes.
Winning the support of smaller factions, such as the Pensioners party, with seven Knesset members, and the left-wing Meretz, with five, would give Livni a stronger mandate to pursue policies that include peacemaking with the Palestinians.
Meanwhile, some 80 truckloads of food and medical supplies were delayed from reaching the Gaza Strip after dozens of Israelis blocked a crossing on Sunday, demanding their government seal an agreement with Hamas to release Gilad Shalit.
Hamas is demanding the release of 1,400 prisoners in exchange for Shalit, the Israeli soldier captured by Palestinian fighters more than two years ago.