India and Russia have yet to finalise terms, such as the payment currency, for the imports, the source said, declining to be named because of the sensitivity of the matter.
"Joint negotiations of state refiners with Russia are already happening," the source said.
Indian private refiners Nayara Energy and Reliance Industries (RELI.NS), opens new tab have already signed term deals for Russian oil imports. Nayara is part-owned by Russian oil major Rosneft (ROSN.MM), opens new tab.
Indian private refiners may join the negotiations with their state-run peers later, the source said.
Asia's third-largest economy needs "predictable and stable" oil supplies as it is expanding its refining capacity to meet rising fuel demand, the source said.
Russia is the top oil supplier to India, the world's third biggest oil importer and consumer.
India has emerged as the biggest buyer of Russian seaborne oil sold at a discount as Western entities have shunned purchases due to a raft of sanctions imposed on Russia over its February 2022 invasion of Ukraine.
During Prime Minister Narendra Modi's visit to Russia this week, India had sought energy deals with Rosneft (ROSN.MM), opens new tab and other leading Russian oil firms.