A memorandum of understanding (MoU) will be signed by Nasser on Wednesday, the sources said.
Aramco, like other major producers, wants to tap rising demand growth and invest in the world's third-biggest oil consumer. Last year it opened an office in New Delhi.
The government outlined plans in February to expand its refining capacity by 77 per cent to about 8.8 million bpd by 2030.
"There are some last minute negotiations on small issues, but both countries are almost ready to announce a deal," the first source told Reuters.
Aramco did not immediately respond to a request for comment.
Representatives of Aramco held a marathon meeting with their counterparts from Indian companies on Tuesday.
B. Ashok, chief executive officer of RRPL, who attended the meeting with Aramco declined to comment on the discussions.
Saudi Aramco, the world's biggest oil producer, is moving to invest in refineries overseas to help lock in demand for its crude, and expand its market share ahead of an initial public offering that is expected later this or next year.
During a visit to Delhi in February, Falih had said Saudi Arabia would also sign oil supply deals as part of the agreement to buy stakes in Indian refineries, a strategy the kingdom has adopted to expand its market share in Asia and fend off rivals.
Last year, Saudi Arabia pledged billions of dollars of investments in refinery projects in Indonesia and Malaysia that came with long-term crude oil supply deals.
Saudi Arabia is competing with Iraq to be India's top oil supplier. Iraq displaced Saudi Arabia for the first time on an annual basis in 2017, data compiled by Reuters showed.
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