The alliance would give Netanyahu's government stronger international support because of Livni's stated commitment to the establishment of a Palestinian state.
Yoel Hasson, a senior Kadima legislator, said that the party "would be happy to renew unity talks" with Netanyahu, but on condition any joint government set Livni's goals as policy.
Reports of the development emerged as Netanyahu appeared on the verge of forming a narrow government with ultra-nationalist and religious parties that would likely take a harder line on concessions to the Palestinians than Kadima.
Livni said after her last round of coalition talks with Netanyahu two weeks ago that Kadima would not sit in a coalition that was not committed to negotiations on Palestinian statehood.
"We have our stands and our principles on the diplomatic front and others and we won't budge"
Gil Messing, an adviser to Tzipi Livni
She also has said she would only join Netanyahu's government if he let her serve as prime minister for half of the government's four-year term.
Netanyahu rejected the proposal.
Dina Libster, Netanyahu's spokeswoman, said on Friday that the two camps "exchanged messages through intermediaries", but did not disclose the content of those messages.
Gil Messing, an adviser to Livni, said that although envoys from Likud party have been trying since the February 10 elections to persuade Kadima to join the government, there would be "no sit down unless Netanyahu agreed to accept Kadima's positions".
"We have our stands and our principles on the diplomatic front and others and we won't budge," Messing said.
Without Kadima, Netanyahu appears able to muster the parliamentary backing of no more than 65 legislators in the 120-seat parliament, meaning almost any member of the coalition could bring down the government in the event of a disagreement.
Netanyahu has until April 3 to piece together his government.