The list has not been finalised as yet, but both the sources said Jaitley was the only one among them who had the credentials to be finance minister. About 35 government ministers are likely to take the oath of office along with Modi, one of the sources said.
It did not include Arun Shourie, another contender for the finance minister's post, the two sources in Modi's Bhartiya Janata Party (BJP) with knowledge of the list told Reuters.
"Jaitley is almost certain to get finance," said one of the sources.
Jaitley, 61, is one of the top corporate lawyers in the country and has served in a previous BJP administration as commerce minister.
However, there is an outside chance that Modi retains the finance post himself with Jaitley getting some other portfolio, another party source said.
The outgoing cabinet of the Congress party government had 70 ministers.
Modi announced late on Sunday that he would streamline the cabinet, a move to a more centralised system of governing that is aimed at breaking decision-making bottlenecks widely blamed for dragging down India's economic growth in recent years.
Modi said he would appoint super ministers in charge of several departments to make ministries coordinate better.
"The focus is on convergence in the activities of various ministries where one cabinet minister will be heading a cluster of ministries who are working in complimentary sectors," he said in a statement.