Elliott wrestled control of Telecom Italia's board away from Vivendi earlier this year, after a two-month campaign to overhaul the way the Paris-headquartered firm had been running the company.
In addition to a governance shake up, Elliott proposed a spin-off and a partial sale of a soon-to-be created network company, a return to dividends and several asset sales.
However, since the New York-based fund took control of Telecom Italia in May, the share price of the former telecoms monopoly has tumbled 35 percent. This despite Elliott having promised to double it within two years, Vivendi said in a statement last week.
France's Vivendi also said it was "deeply concerned by the disastrous management" at Telecom Italia in recent months, adding the company's figures were suffering as a result.