There was no immediate confirmation from Peres, who was attending a football "peace match" in Barcelona, Spain, pitting a team made up of Israelis and Palestinians against the Spanish side.
According to Channel 10 the move would entail Peres giving his support to Sharon's new party in next year's general election, but would not see him formally joining the party.
The station said Peres conveyed his decision to one of its reporters accompanying him on a trip to Europe where he attended a football "peace match" in Barcelona, Spain, on Tuesday pitting a team made up of Israelis and Palestinians against a Spanish side.
Channel 10 correspondent Gilad Yadin said Peres had decided to leave Labour, which expelled him as leader in a 9 November primary election, and "embark on a new political path".
The 82-year-old Nobel peace laureate would announce his support for Sharon and Kadima on his return to Israel on Wednesday, but would not become one of its members, Yadin said.
Peres would also not run for parliament in the coming poll, the reporter said. Under Israeli law, that would not bar him from accepting a cabinet post.
Public radio also said that Peres would opt to support Kadima "from outside".
Ousted Labour leader
Twice prime minister, but never elected to the position, Peres was visibly stunned earlier this month when firebrand trade union chief Amir Peretz drove him out as Labour Party leader in a primary election.
Israeli media reports said Sharon would offer Peres the job of peace envoy if the new Kadima party won the 28 March poll.
Peres (C) was in Barcelona to
support a football 'peace match'
Sharon, in a gamble that could reshape Israeli politics for years to come, quit the Likud Party last week, saying he could not push for peace with the Palestinians while "wasting time" battling far-right rivals in the movement he co-founded in 1973.
At the same time, he has reaffirmed a pledge to keep major Jewish settlement blocs in the occupied West Bank in any future peace treaty, a prospect Palestinians said would deny them a viable state.
Peres's support for Sharon would represent an earthquake with the potential to bring down the decades-long political structure that has left Israel stalemated between hawks and doves - led by Labour and Likud.
Electoral deadlocks over whether to compromise with the Palestinians have led to five elections in 10 years - political instability that has hamstrung not only most peace efforts, but also killed chances of long-term programmes to heal Israel's domestic ills of poverty, declining education standards and increasing violence.
"In my eyes it's not a problem of parties but a problem of peace - how to create a strong coalition for peace"
ousted Labour leader
As Labour Party leader and Israel's vice-premier, Peres helped Sharon to complete a unilateral pullout of troops and Jewish settlers in Gaza last September, despite protests in the Likud that such a withdrawal only rewarded Palestinian violence.
Speaking to reporters in Barcelona on Monday, Peres said he would announce his decision after his return home.
"In my eyes it's not a problem of parties but a problem of peace - how to create a strong coalition for peace," Peres said.
Peres has jumped ship before. In 2000, rebuffed by the then prime minister Ehud Barak in his attempt to recapture the Labour Party nomination, Peres offered to run as a Meretz Party candidate, but the dovish Meretz refused and Peres returned to Labour.
In 1965, Peres followed David Ben Gurion, his mentor and
A Palestinian-Israeli team played
Barcelona in the peace match
Israel's first prime minister, into a new party called Rafi. It received only 10 seats in the 1965 election and rejoined Labour three years later.
Opinion polls show Kadima besting Labour and the Likud in the 28 March ballot.
In a significant political move on Tuesday, Dalia Itzik, a Peres ally and a former communications minister, joined ranks with Kadima.
In his bid to appeal to a broad cross-section of Israelis, Sharon has courted support from an odd alliance of people, from Israeli Arab leaders to a former security chief who expanded a policy of assassinating Palestinian resistance leaders.
Fourteen Likud legislators have already defected to his new party.