However, no official announcement has so far been made regarding Oli's proposed visit to India, the Kathmandu Post reported.
Citing sources at the Nepali Embassy in New Delhi and officials at India's External Affairs Ministry, the paper said that dates of Prime Minister Oli's India visit have been "under active consideration" since he assumed office more than a month ago.
The formal announcement will be made once the Nepali side gives its concurrence to the proposed date-April 6-8, according to a senior official in Kathmandu.
A source at the Indian Embassy in Nepal also hinted towards a likely visit by Oli in the first week of April.
While congratulating Mr Oli over phone upon his appointment to the top executive post, Prime Minister Narendra Modi had extended an invitation to him for a visit to India.
External Affairs Minister Sushma Swaraj had visited Nepal before Mr Oli took office to congratulate him for the historic victory of the Left Alliance in the Parliamentary and Provincial elections.
Ms Swaraj was the first senior Indian minister to visit Nepal after the conclusion of elections to local bodies, provincial assemblies and federal Parliament.
Mr Oli, widely regarded as pro-China, last month said he wants to "update" relations with India "in keeping with the times" and favours a review of all special provisions of the Indo-Nepal relations, including the long-established practice of Nepalese soldiers serving India's armed forces.
It is natural for Prime Minister Oli to visit India first as it signifies that the Left Alliance government accords top priority to Nepal's relations with the southern neighbour, a senior leader of ruling CPN-Maoist Centre told PTI.
The formal announcement will be made once both sides work out the detailed itinerary of the proposed visit, the sources said.
Foreign Minister Pradip Gyawali is likely to visit New Delhi ahead of Oli's official trip to prepare ground for the visit.