Mr Netanyahu, said to favour early elections in a bid to strengthen his position before a potential fight over austerity measures and US elections in November, has so far made no official announcement on a change to the date, currently scheduled for October 2013.
"Apparently the Knesset will decide on elections within the coming days," Mr Barak, a close confidante of Mr Netanyahu, was quoted by his office as telling members of his Independence party on Monday.
"Whether the elections themselves are set for the middle of August or the middle of October I don't see much difference. We are entering an election campaign."
"It's final," said Foreign Minister Avigdor Lieberman, who heads the ultra-nationalist Yisrael Beitenu party. "Now it is only a question of dates."
Mr Lieberman, whose party is a key partner in Mr Netanyahu's coalition government, told the Ynet news website that he was eager for the vote to take place as quickly as possible.
"If the decision to go to elections has been made, we should hold them as quickly as possible," he said.
Israeli public radio said Mr Netanyahu favours a date between mid-August and the beginning of September, while the head of the main opposition Kadima party, Shaul Mofaz, is pushing for October 16.
Commentators said there were plenty of reasons for Mr Netanyahu to favour bringing the vote forward, including the desire to consolidate his position before having to implement budget cuts later this year.
He is also looking to bolster domestic support before US elections in November, which could return US President Barack Obama to office.
Mr Netanyahu has differed with Mr Obama on issues ranging from the stalled Israeli-Palestinian peace process to Iran's nuclear programme.
Another key reason for bringing the vote forward is a dispute over the issue of drafting Orthodox Jews into the army, which has threatened the stability of Mr Netanyahu's coalition.
The so-called Tal Law, which allowed ultra-Orthodox Jews to defer their service in the Israeli military, is strongly opposed by Lieberman's staunchly secular Yisrael Beitenu party.
Mr Netanyahu has pledged to replace the law, which expires this year, with a more "egalitarian" rule, but is caught between Yisrael Beitenu and the ultra-Orthodox factions in his coalition, who adamantly oppose military service.
The Knesset is expected to debate a replacement law on May 9.
Whenever the elections are held, polls have consistently showed Mr Netanyahu and his Likud party coming out on top, with no credible rival to the prime minister.
A poll published by the Yediot Aharonot newspaper on Monday showed Likud increasing its strength from 27 to 30 seats in the 120-seat Knesset, if elections were held today.
The Labour party stands to make the biggest relative gain, winning 18 seats, from the nine it currently holds, while Yisrael Beitenu would lose two seats, leaving it with 13, the poll showed.
Kadima is expected to suffer crushing losses, with its standing reduced from 28 seats to 11, while the newly formed Yesh Atid (There is a Future) party would win 11 seats, the poll found.
The shape of any future coalition remains unclear, however, with Labour, Kadima and Yesh Atid all having expressed willingness to join a government led by Mr Netanyahu.