The German company revealed the prospective move in a disclosure filed with the U.S. Securities and Exchange Commission (SEC).
In the SEC submission RWE said if they were to go ahead with the sale the timing would depend on market conditions. The sale could be in the form of public or private stock sales, reorganisation or a merger.
RWE's share of Pittsburgh-based CONSOL is worth about US$1.25 billion.
The Charleston Gazette reported vice president and spokesman for CONSOL Tom Hoffman said a sale of RWE's shares was far from certain and that the German company's SEC announcement was "fairly broad."
"They reserve the right at the end of the day to do nothing. Until the RWE folks sort out what they want to do, and provide more clarity, the market reaction has been mild," Hoffman said, according to the Charleston Gazette.
CONSOL is the biggest operator of underground coal mines in America, with 14 of the 57 longwalls in operation last year. The company produces more high-Btu bituminous coal than any other producer in the United States.
Large underground operations are located in northern and central Appalachia coal basins, the Illinois basin and in Western region in Utah.
CONSOL reported a 2002 net income of about US$11.7 million, down significantly from US$151 million in 2001 where they produced 73.7 million tons of coal and 38.0 Bcf of coalbed methane.