"We have to have a fair equilibrium" between the two parties, he added.
Netanyahu has so far rejected the rotating premiership option.
Although Kadima gained 28 seats in parliament in last week's general election - one more than Likud - Netanyahu is widely tipped to become the next prime minister.
Under Israeli law, the person charged with forming a ruling coalition in the 120-seat Knesset (Israeli parliament) is not necessarily the election winner, but the one with the greatest chance of forming a government.
Netanyahu, with support from fellow right-wing parties that dominated the February 10 vote, has the support of 65 seats in the chamber, whereas Livni has the backing of 44.
But Netanyahu is thought to prefer a broad coalition that would include Kadima.
Livni has so far insisted that she should lead any unity government.
"I have already been number two and, from that position, I will not be able to advance procedures," she said during closed talks, according to the Israeli news service, Haaretz.
Ehud Olmert, the Israeli prime minister, has urged Livni to go into opposition rather than join a Netanyahu-led administration.
"Go into opposition and you will steer Kadima to victory in the next elections," the local press quoted Olmert as telling Livni on Sunday.
If Kadima goes into opposition, Netanyahu will be forced to form a coalition with Avigdor Lieberman of Yisrael Beitenu, as well as ultra-Orthodox parties and extreme right-wing settler groups.
Such a government could put Netanyahu at odds with Barack Obama, the US president, who has sent an envoy to the region to vigorously pursue Middle East peace talks.
Likud on Sunday urged Kadima to join a Netanyahu-led cabinet.
"It is unfortunate that Livni will not set petty politics aside and consider national interests as a top priority," it said in a statement.
Official results from the election will be published on Wednesday.
Shimon Peres, the Israeli president, will then have seven days before which he will select a member of parliament to form the next ruling coalition.