The block Abai, which was previously being operated by Statoil of Norway, is adjacent to OVL's Satpayev exploration block.
Kazakhstan made the offer at the meeting of the Joint Working Group in Astana late last month, official sources said.
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OVL, the overseas arm of state-owned Oil and Natural Gas Corp (ONGC), has been offered 25% interest in the Abai block, which according to Kazakhstan government estimates has 2.8 billion barrels of oil reserves.
However, the Indian firm believes the reserves may not that high and will study the data before accepting the offer, they said.
Kazakhstan had last year blocked OVL's $5 billion deal to buy an 8.4% stake in the Kashagan oilfield from US energy giant ConocoPhillips. Kazakhstan exercised its pre- emption right to first buy the ConocoPhillips' stake and then sell it off to Chinese firm CNPC.
In 2005, India had lost a $4.18 billion deal to buy PetroKazakhstan to China.
"They (Kazakhstan) realise that they were more than unjust to India and have put all their eggs in one basket ie China. And so they are now making overtures," an official said.
Statoil had in February 2013 given up the Abai offshore block spending about seven years negotiating to start exploration.
State-owned KazMunaiGaz National Co held 75% interest in the block with an estimated 387 million tons of resources (2.8 billion barrels). Statoil had 25% interest which is now being offered to OVL.
Delays and cost overruns have dogged Kazakhstan's efforts to expand offshore production of oil and gas. OVL had planned to drill two exploration wells on Satpayev in 2014 and 2015 but delivery of a drill rig has been delayed and will now be available only next year.
OVL bought 25% of Satpayev in 2011. It paid $13 million as a signing amount to Kazakhstan. In addition, it will pay $80 million as a one-time assignment fee to KazMunaiGas (KMG). On top of this, OVL had committed a minimum exploration investment of $165 million and an additional optional expenditure of $235 million to the project.
The Satpayev block, measuring 1,582-square kilometer, is located in the North Caspian Sea, in water depths of 6-8 metres, and has two prospective areas that hold an estimated 256 million tonnes of oil and natural gas resources. It lies near four major discoveries.
OVL estimates a peak output of 287,000 barrels per day from the Satpayev and Satpayev Vostochni (East) structures.