The Times of India reported earlier that Aramco was in talks to buy a stake of up to 25 percent, which could be worth around $10-15 billion, valuing the Indian company's refining and petrochemicals businesses at some $55-60 billion.
Aramco's discussions with Reliance were "serious", one source said. Another source said talks with Reliance were so far for a 25 percent stake.
"Reliance has offered an integrated deal - a stake in existing refineries and the planned 600,000 barrels per day (Jamnagar) refinery, along with petrochemical business," the second source said.
Aramco's chief executive, Amin Nasser, said in February that the Saudi company was in talks on possible investments in Indian projects involving firms that included Reliance.
Aramco and Reliance declined to comment on Wednesday.
Reliance, controlled by Asia's richest man, Mukesh Ambani, is India's biggest refining and petrochemicals company and runs a 1.4 million barrels per day refining complex at Jamnagar in western India. It plans to expand capacity to 2 million bpd by 2030, according to plans shared with the Indian government.
Aramco is expanding its refining and petrochemical business globally by signing new deals and boosting the capacity of its existing plants.
Last year, Aramco and the United Arab Emirates' national oil company ADNOC teamed up with state-run Indian refiners in a plan to build a 1.2 million bpd refinery and petrochemical project in Maharashtra state.
However, the planned refinery faces delays, as thousands of farmers have refused to surrender land for it and the Maharashtra government is looking to move the plant's location.
Saudi Crown Prince Mohammed bin Salman visited India in February and said then that he expected investment opportunities worth more than $100 billion there over the next two years.
Ambani has travelled to Saudi Arabia at least twice since December, discussing joint investment among other issues with Aramco's chief executive, Amin Nasser.