Addressing members of Kadima's parliamentary faction, Olmert said the 83-year-old Nobel Peace Prize laureate would be able to restore the prestige of the largely ceremonial post, undermined by recent allegations of rape and abuse of office against the incumbent, Moshe Katsav.
Peres, who lost his presidential bid as a Labor leader to the right-wing Likud's Katsav in 2000, is expected to confirm his intention to run again in an official announcement Wednesday.
Israel's president is elected by the country's parliament, the Knesset, for a term of seven years.
Peres joined Kadima in 2005, and will now be vying for the office against Labor candidate Colette Avital and former Knesset spokesman Reuven Rivlin, of Likud.
He served as prime minister in 1984-1986 and 1995-1996, and won the 1994 Nobel Peace Prize for his role in forging interim peace deals with the Palestinians.
Katsav, currently on a leave of absence, may face criminal action on rape and abuse of office charges once he hands over to a successor.
