Deuba, 69, was elected president of the largest democratic party in Nepal in March during the party's 13th National General Convention, succeeding late premier Sushil Koirala.
Although a Deuba aide said the India visit beginning today was for medical check up of his wife and NC lawmaker Arzoo Deuba, it is widely speculated here that he may have some high-level meetings with Indian leaders during the visit.
This will be the three-time former prime minister's first visit to New Delhi after the promulgation of the Constitution last year.
Following the promulgation, Nepal has been gripped by a severe political crisis as disgruntled Madhesi parties, who have a stronghold in the southern plains, began an agitation alleging that their interests have been overlooked in the new charter.
Though the six-month agitation abruptly ended in February ahead of Prime Minister K P Sharma Oli's official visit to India, some Madhesi leaders appeared unsatisfied with the compromise offered by the government.
Previously, Madhesis, who are largely of Indian-origin, had staged violent protest campaigns and also imposed a trade blockade through the open border with India.
Deuba has been calling for a peaceful resolution to the Madhesi problem through dialogue.
Ahead of the visit, Deuba met senior Madhesi leaders at his residence on Friday and discussed their demands.
Earlier, speaking at a public function in the capital Kathmandu, Deuba said the main Opposition Nepali Congress will take a leading role in resolving the Madhesi issue.