JERUSALEM, Oct 31 (Reuters) - Former leaders Ehud Olmert and Tzipi Livni announced on Wednesday they were discussing a partnership that could shake up Israeli politics and lead to a joint campaign to defeat Prime Minister Benjamin Netanyahu in a January election.

Olmert, a centrist, was forced to quit as prime minister in 2008 over corruption charges of which he was largely acquitted.

Were he to make a comeback, he is seen as possibly the most likely candidate to beat Netanyahu, the right-wing Likud party leader, who polls now predict will win re-election.

Livni, who quit the centrist Kadima party in March after a failed leadership contest and headed Middle East peace talks which deadlocked months after Netanyahu took office, is also seen as a strong potential contender for Israel's Jan. 22 race.

A statement from an aide to Olmert said he and Livni had agreed "action must be taken to change the leadership", citing what it called "Israel's deteriorated status" under Netanyahu. It alluded to tensions with the United States about how to rein in Iran's nuclear programme and diplomatic paralysis with the Palestinians.

Both agreed to continue meeting and a confidant who spoke on condition of anonymity confirmed Israeli media reports that they were weighing the prospect of a joint election run. A Livni aide also confirmed these talks took place.

It was not clear whether the pair would join one of Israel's centre or left-leaning parties, or form their own.

Olmert and Livni once headed the centrist Kadima party, whose popularity has nosedived under their successor, former general Shaul Mofaz.

Founded by former prime minister Ariel Sharon, the party is now predicted to win only a handful of seats in parliament in the coming election, latest surveys show.

But Olmert and Livni may seek to tap into dissatisfaction among moderates in Netanyahu's right-wing Likud party over Netanyahu's union this week with far-right Foreign Minister Avigdor Lieberman, now running jointly in the coming election.

Despite the critics, the latest polls show Netanyahu winning as many as 42 seats in Israel's 120-member parliament which would assure him of heading the country's next coalition government.