As per media reports, incumbent PM Sushil Koirala is likely to submit his resignation on Friday as the Nepal Parliament session has been called to elect the new PM of the Himalayan nation.
Oli, 63, had earlier conveyed his dismay at India's reaction to Kathmandu adopting a new constitution.
"We are very concerned with the cracks in relationship that are visible," Oli, told IANS in an Interview at his residence at Kathmandu.
Oli said there was "some misunderstanding at present" between the two countries over the new Constitution which Nepal adopted recently.
India has urged that the Constitution be amended to take care of rights of all sections of the country, including Madhesis who are largely settled in the Terai region of the country.
Oli said there was no movement in Terai areas of Nepal and some groups were being used for violence. He said the whole world welcomed Nepal's adoption of the constitution after prolonged efforts but India merely took note of it.
Communist Party of Nepal-Unified Marxist-Leninist (CPN-UML), the second largest party in the coalition government, had projected Oli as the next prime ministerial candidate.
Nepal's Deputy Prime Minister Bamdev Gautam had said in June that the government to be formed after the promulgation of the new constitution will be headed by CPN-UML.
Nepal adopted a new Constitution on Sunday which states that the federal and secular Nepal will have seven provinces, each with its own legislature.
Nepal's first Constituent Assembly was dismantled in 2012 with political parties differing over majour issues like system of state governance and number of federal units.
The second constituent assembly elections were held in 2013. The constitution-making process was apparently hastened after the devastating earthquake in Nepal earlier this year in which about 8,500 people were killed.
The Maoists had won the elections to the Constituent Assembly in 2008 leading to abolition of over two centuries of monarchy.
(With inputs from agencies)