The Times of India and the Hindustan Times reported earlier that Modi, who swept to power in a general election last month, had already accepted the invitation for talks in September.
But the source told Reuters the final details of the visit, proposed by Obama when he called to congratulate Modi on his general election victory on May 16, had not yet been set.
"We are working on dates with the USA," the source said. "They went out of the way."
The U.S. embassy declined to comment ahead of a visit by U.S. Assistant Secretary of State Nisha Biswal to New Delhi on Friday for the first meetings with the new administration since it took office.
Biswal is expected to meet Foreign Minister Sushma Swaraj and it is possible that Modi's trip could be announced at the end of her visit.
India and the United States are keen to boost security and economic ties, and the Obama administration has set a goal of quintupling annual bilateral trade to $500 billion.
The summit would mark a significant upgrade from what was earlier expected to be an encounter between Modi and Obama on the sidelines of the annual U.N. general assembly in New York.
Modi, 63, a former chief minister of Gujarat, was refused a U.S. visa over sectarian strife in the western Indian state in 2002 in which more than 1,000 people, mainly Muslims, were killed. He has denied any wrongdoing and an Indian Supreme Court inquiry found no case to answer.
The U.S. ambassador to India met Modi earlier this year, as opinion polls put his Bharatiya Janata Party (BJP) on course for an election victory. U.S. officials had said a visa and an invitation to meet would probably be forthcoming if Modi won.
Modi wants to cautiously open up the Indian economy to foreign investment to boost growth and job creation.
His new government is expected to announce that it will allow foreign online retailers to sell their own products in India, a major business opportunity for players such as Amazon.
Lisa Curtis, a South Asia specialist at The Heritage Foundation, said a Modi visit would be an opportunity to put U.S.-India trade ties back on track. The two countries have sparred in recent months over trade policies and patent laws.
"President Obama made a good move by inviting Narendra Modi to visit Washington and he has reciprocated by accepting the invitation," Curtis told CNN-IBN TV news.
India is widely perceived in Washington as a serial trade offender, with U.S. firms unhappy about imports of everything from shrimp to steel pipes, which they say threaten jobs, as well as a lack of fair access to the Indian market.
New Delhi has urged the Obama administration not to fall prey to special interest groups and consider trade issues in the context of wider economic and strategic ties between the two nations.