Gandhi, president of the ruling Congress party and widow of former premier Rajiv Gandhi, is the influential patron behind Prime Minister Manmohan Singh who has led India since 2004.
Party officials announced on August 4 that Gandhi, 64, had undergone surgery in the US, though they have since declined to release any further information about her health or where she was admitted to hospital.
"Sonia Gandhi will be returning soon but I cannot say whether she is coming tonight or within the week," Congress party spokesman Janardhan Dwivedi said.
Italian-born Gandhi is widely thought to be preparing the ground for her only son Rahul to become prime minister at some stage after Singh, 78, steps down.
Rahul, 41, who sits in the lower house of parliament, has had joint charge of the Congress party while Sonia has been away, but he adopted a low profile during a major government crisis over nationwide anti-corruption protests.
"Sonia Gandhi is recovering well post-surgery and will return from the United States this week, accompanied by her daughter Priyanka Vadra," the Press Trust of India news agency said on Tuesday, citing unnamed sources.
The Congress party has been criticised in the Indian media for a lack of transparency over Gandhi's operation and her recovery. It insisted her health was a private matter.
The Nehru-Gandhi dynasty, which has no link to independence hero Mahatma Gandhi, has exerted huge influence in India since Jawaharlal Nehru became the country's first prime minister after independence from Britain in 1947.
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May she never returns..
I wish Ms. Sonia Gandhi health & speedy recovery. The key to peace in South East Asia rests on her shoulders.
She has cervical cancer