She is expected to officially launch her candidacy on July 19, the spokesman said.
It is unclear why the president, a widely popular leader who has restored the Argentinean economy to healthy position following the crash of 2002, would decline to run for re-election.
Commentators have cited reasons ranging from health problems to a plan to compete again in 2011.
Christopher Sabatini, director of policy for Council of the Americas, a business organisation in the United States, told Al Jazeera: "Most people thought he would run. It surprised most people. Of the two, he is much more popular.
"There is an idea of a Kirchner dynasty. According to the Argentinean constitution you can only run two consecutive terms. If they were to shift back and forth this could go on indefinitely."
The Argentinean president's approval rating fell in June to 52 per cent from 57 percent in May - the lowest level of his presidency - according to a survey by Buenos Aires-based Poliarquia.
Argentina's first lady has been travelling abroad on official visits that are seen as an attempt to boost her profile and her chances of becoming the country's first elected female leader.
In mid-June, she was in Europe, meeting figures including Pascal Lamy, the World Trade Organisation chief. She has also travelled to France, the US, Mexico, Venezuela and Ecuador in the last six months.
She was a better known politician than her husband when he ran for president in 2003.
The couple have drawn obvious comparisons with Bill Clinton, the former US president, and his wife, Hillary Clinton, a senator and contender in the 2008 US presidential election.