Italian-born Gandhi will meet President Abd al-Kalam on Monday armed with letters of support from several parties to stake her claim to government after ousting the ruling Hindu nationalists in India's biggest election upset last week.
Leftist parties, which won a pivotal 60-plus seats in the election have pledged their support for Gandhi, but were debating on Sunday whether to formally join her coalition or simply back it from outside.
The communists are also discussing a joint economic policy with an eye to reassuring investors after the rupee and shares crashed on Friday to their lowest in months.
Gandhi's Congress party has secured enough support from its allies almost to guarantee she will be the next prime minister - and India's first foreign-born leader.
"I thank the people of India from my heart. We have succeeded against all odds, we have prevailed despite all predictions of disaster"
She will also be the family's fourth prime minister after her slain husband, Rajiv, mother-in-law Indira and Indira's father Jawaharlal Nehru.
Despite routing Prime Minister Atal Behari Vajpayee and his Bharatiya Janata Party, Congress fell short of a majority in the 545-seat parliament and Gandhi has been in hectic negotiations to settle on the size and shape of her coalition.
So far, the left is divided on whether to join Gandhi. Some communist groups are in direct opposition to the Congress at the state level.
However, their support is critical. The leading leftist group, the Communist Party of India (Marxist) is the largest in the new parliament, with 43 seats, after Congress and the BJP.
"I thank the people of India from my heart. We have succeeded against all odds, we have prevailed despite all predictions of disaster," Gandhi said on Saturday after Congress chose her as its parliamentary chief.
"There is now a momentum generated by our revival, let us not squander it. We must utilise it as a catalyst for change."
Congress, which first put India on the path to reform by ditching its socialist economics a decade ago, has pledged to continue Vajpayee's programme of economic modernisation, but with "a human face".
But investors fear the leftists will block or slow reforms, especially the sale of bloated, monolithic state firms.
The communists, who have copied Chinese-style reforms in the states they govern, tried to appease markets on Saturday, saying they welcomed foreign investment and realised no country could quarantine itself from the globalised economy.
India's poverty-stricken masses
made Vajpayee pay with his job
Analysts also expect Gandhi's government to repackage the reforms after India's hundreds of millions of poor punished Vajpayee and the BJP for failing to pass on the benefits of a booming economy, which instead went mainly to the relatively small urban middle class.
Gandhi's victory marked not just the revival of India's oldest party, but of the Nehru-Gandhi dynasty as well, with the political debut of her son, Rahul, and daughter, Priyanka.
Rahul Gandhi easily won his seat in the family borough. Priyanka did not stand, but played a major role in campaigning.
In all, the family has ruled the world's second most populous nation for 35 of the 57 years since independence.