The fund said in November it would sell shares to dilute its 78.02 per cent stake in Essar Energy so the company met UK listing requirements, which mandate that at least 25 percent of a company's stock be available for trading.
Since then, Essar Energy's shares have lost about 38 percent of their value until Thursday. They closed up 10 percent on Friday.
Essar Global said on Friday it could make an offer on its own or as part of a consortium at a "modest" premium to Essar Energy's Thursday close of 60 pence on the London Stock Exchange.
Essar Energy declined to comment.
The company's second-largest shareholder, Capital World Investors, said it could not disclose if it planned to participate in a bid.
Essar Global said there was no certainty it would make an offer, and until then it would not transact in the shares of the company even to meet the free float requirement.
Essar Global also said it may offer to buy Essar Energy's 4.25 percent convertible bonds due 2016.
The oil and gas company is controlled by privately held Indian conglomerate Essar Group, which has interests in steel, shipping, power and other sectors.
Essar Energy's shares closed at 66 pence, making the stock one of the top percentage gainers on the FTSE-250 Midcap Index.