The letter from Ben Walker, a partner at hedge fund TCI said that Dassault, the maker of the Falcon business jet and the Rafale fighter jet, is, for the European Aeronautic Defense and Space company a "poor use of capital."
The New York Times reported Monday that TCI owns just over 1 percent of EADS.
"As soon as possible," was the recommended time line in Walker's letter, the Times said.
"We will keep shareholders fully appraised of our plans and progress. Central to our strategy is efficient capital allocation and creation of shareholder value," said EADS spokesman Martin Aguera in a public response to the letter.
But an industry analyst said divesting itself of Dassault would be easier said than done, given the company's political connections, its defense contracts and the point that two-thirds of the company's 11,600 employees work in France.
"Politics will play a large part in this," said Howard Wheeldon, an independent analyst and a fellow of Britain's Royal Aeronautical Society.
Wheeldon noted that a non-French buyer would not be easily accepted.
As a back up plan, the French government has first rights for buying shares in the company, which is valued at about $5.5 billion.
But coming up with that sum or a substantial portion would be a high hurdle for the French socialist government, the newspaper said.
"Dassault is a relatively small, under-capitalized company in what is an increasingly very large and high-risk world of key defense products," Mr. Wheeldon said. "EADS potentially walking away is, for Dassault, a very worrying sign."