The absence for a month of the 64-year-old, India's most powerful politician, has caused serious problems for the government, accused of mishandling the biggest protests in decades and worsening ties with parliamentary allies.
Broadcaster NDTV, citing Congress party sources, said the Italian-born Sonia Gandhi was expected to return to the capital on Tuesday, but it was not clear when she would return to work.
The Times of India, without citing any sources, said: "She is likely to need at least another couple of months for a full recovery."
Congress has declined to comment on the nature of her illness, which required surgery in the United States. However, several media outlets have said she was treated for cancer at the Sloan-Kettering Cancer Center in New York.
When contacted by Reuters, a Congress spokesman declined to comment.
Gandhi's return will be good news for the beleaguered government, which looked indecisive during the anti-corruption protests led by 74-year-old activist Anna Hazare who forced the government to back down and agree to tougher anti-corruption legislation.
After leaving for surgery, Gandhi promoted her son Rahul to help manage the party in her absence. He is widely expected to be the next prime minister if the Congress party returns to power in 2014 elections.
Recent opinion polls show support for Congress falling behind the Bharatiya Janata Party.
The Gandhi family, descended from India's first Prime Minister Jawaharlal Nehru, enjoys a status similar to royalty in the country of 1.2 billion. Out of respect, normally clamorous 24-hour news stations have been almost silent on Sonia Gandhi's condition.
Sonia was married to Rajiv Gandhi, Nehru's grandson and a former prime minister, who was killed by a suicide bomber in 1991 while campaigning for elections.
His mother, Indira Gandhi, was also prime minister when she was assassinated by her Sikh bodyguards in 1984.
Despite an aggressive 24-hour news media in India, they have largely stayed away from reporting on Sonia's illness or what her absence meant for running the world's largest democracy.
India's main political parties have also largely shied away from commenting on Sonia's absence.