The public television, without giving sources, said the 82-year-old veteran politician and Nobel peace prize laureate was to announce his decision after returning home from Barcelona.
However, as Mr Peres attended a "Peace Match" in Barcelona in which a team made up of Israeli and Palestinian footballers against the local team, Israeli public radio said that Mr Peres would opt to support Kadima "from outside" rather than formally jump ship.
According to army radio, he has been offered the number two position in the new party list being compiled for a March 28 general election.
Mr Peres, himself a former prime minister, was ousted from the Labour helm earlier this month by trade union leader Amir Peretz who promptly pulled the party out of Mr Sharon's coalition government.
As a result, Mr Peres lost his post as deputy prime minister.
Elections
Mr Sharon announced last Monday that he was quitting the right-wing Likud to form Kadima, having grown exasperated with right-wingers who refused to forgive him for pulling Israeli troops and settlers out of the Gaza Strip.
While the bulk of new recruits to his party have been fellow Likud defectors, Mr Sharon has also managed to attract former Labour cabinet minister Haim Ramon.
Meanwhile Ariel Sharon's new party has announced it is willing to see the creation of a Palestinian state as it feted the defection of two members of the opposition to its ranks.
Kadima will campaign for election in March on a platform of giving up some of the occupied territories to ensure a homogeneous Jewish state.
Presenting party plans ahead of the March 28 parliamentary vote, Sharon confidante and Justice Minister Tzippi Livni said the movement would seek a "demilitarised Palestinian state not involved in terrorism."
A draft manifesto under debate backs the creation of a demilitarised
Palestinian state while seeking to maintain Israeli sovereignty over annexed east Jerusalem and the largest Jewish settlement blocs in the West Bank.
Successive Israeli governments have insisted on retaining Jerusalem as its undivided and eternal capital, despite no international recognition of its annexation of the Arab eastern sector which it captured in 1967.
Kadima also wants wildcat outposts all over the West Bank, seen by many Jews as an integral part of the land of Israel, dismantled at once.
The West Bank is far more populous and Biblically important than Gaza, from which Mr Sharon withdrew all Israelis in September.
Palestinian deputy prime minister Nabil Shaath dismissed Kadima's posturing as "merely campaign slogans" of no concern to the Palestinians.
"We know that there will be no peace without an independent Palestinian state with Jerusalem as its capital and a just and agreed solution to the refugees," he said.
Kadima ahead
With his party ahead in opinion polls and a majority of Israelis willing to trust Mr Sharon with the nation's security, the prime minister could however lose ground over pressing social and economic issues.
In a country where 1.5 million people live below the poverty line and unemployment stands at nine percent, a Labour party veering to the left under trade union boss Amir Peretz could pick up votes on domestic issues.
With Mr Sharon campaigning for as broad a consensus as possible, his party's prospects brightened as the founder of Israel's secular Shinui party and a second senior Labour MP raised to 18 the number of lawmakers in his new venture.
Former communications minister Dalia Itzik, a close ally of Mr Peres, who resigned her position last week when all Labour ministers left Sharon's shaky coalition, said she was leaving Labour to join Kadima.
"For years we have had no element to tip the balance between the two blocs. And suddenly this man (Sharon), by his image and actions, succeeded in rising above those traditional voting patterns," she said.
Uriel Reichman, the president of Shinui who founded the party and recruited Holocaust survivor Tommy Lapid to head the movement, will also join Mr Sharon's party as a candidate for education minister.
His defection is likely to serve a heavy blow to Shinui's public standing.
One recent poll predicted that Kadima could wipe the secular, middle-class party off the political map, losing 10 of its 15 seats in parliament.