Rajinikanth's daughter Soundarya visited the Tiruvottiyur Shri Vadivudai Amman Temple in Chennai to offer prayers for the speedy recovery of her father
Asked whether an announcement scheduled for 0630 GMT was about the sale of a stake, the source said: "Yes."
Industry sources had said in May the DME planned to sell up to 20 percent of itself to help boost liquidity and attract more international players.
The DME launched trading in June 2007 with a sour Middle East crude futures contract, aiming to become the benchmark for pricing in the world's top oil exporting region.
Its flagship Oman crude oil contract has shown little growth since it was launched just over a year ago.
It was not immediately clear whether the company would issue new capital for the stake or whether one of its owners was selling off part of their stake.
NYMEX reached a deal in March to merge with the CME Group Inc, the world's largest derivatives exchange. One source said in May the DME would like to push through the stake sale before the CME merger was completed.
NYMEX and Dubai's state-owned Tatweer each own 32.5 percent of the DME. The Oman government has 30 percent and the remaining 5 percent stake is held by DME floor members.
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