Former Kadima chairwoman Tzipi Livni is pushing President Shimon Peres to run for prime minister.
Ms Livni's associates have confirmed in a statement that she would like Mr Peres, who is 89 years-old, to run because she believes there is no one more worthy to lead the centrist camp.
It is suggested Mr Peres could use his high approval ratings to unify the centre-left parties, the only route to toppling the Netanyahu government. There are conflicting reports as to whether or not Mr Peres has rejected the proposal.
Mr Peres spent the week in Russia, where he urged Russian and US leaders to join forces to stop the nuclear threat to Israel from Iran.
