MILAN—Telecom Italia (TIM) has received a 10.8 billion euro ($12 billion) approach from U.S. fund KKR aimed at taking Italy’s biggest phone group private, the company said on Sunday. KKR’s move comes as TIM’s CEO Luigi Gubitosi battles for survival after coming under fire from top investor Vivendi following two profit warnings in three months. TIM said KKR had set an indicative price of 0.505 euros for its possible buyout offer—a 45.7 percent premium to the ordinary shares’ closing price on Friday. KKR would also offer the same price for TIM’s savings shares. The TIM board, chaired by former Bank of Italy official Salvatore Rossi, met for several hours on Sunday afternoon but in a short statement it gave no indication of whether it would support the approach. It noted that KKR had termed its action as “friendly” and aimed at winning the backing of the company and of the …