MILAN, Dec 6 (Reuters) - Shares in Telecom Italia (TIM) (TLIT.MI) fell on Monday, hit by growing uncertainty over a $37 billion takeover approach by U.S. fund KKR (KKR.N). After receiving KKR"s proposal on Nov. 19 and then losing its fourth chief executive in six years, TIM has failed to make progress in what would be Europe"s biggest ever private equity buyout.Sources have said the management upheaval has complicated decision-making. read more After CEO Luigi Gubitosi lost out in a clash with TIM"s top investor, Vivendi (VIV.PA), veteran manager Pietro Labriola was promoted as general manager. However, a new CEO cannot be named until Gubitosi or another director vacates a board seat.Vivendi declined to comment on Monday, but the previous day it said it was open to handing control of TIM"s fixed network to the state if the group parts with its most prized asset. In the past TIM has said it wanted to retain majority ownership. read more "We understand this change of opinion as a way of hindering KKR"s path," Caixa analysts said. Further muddying the waters, Italian press at the weekend reported a meeting between Vivendi and state-owned investor CDP, TIM"s second-largest shareholder, over a possible alternative plan to KKR"s. Two sources close to the matter told Reuters that Vivendi was trying to build an alliance with CDP. Trying to revive a project that stalled under Prime Minister Mario Draghi, the Treasury is still studying a possible merger between TIM"s fixed network and state-backed rival Open Fiber under CDP"s control, a source directly involved in the matter said last month. However, Draghi is not actively involved in talks at present and there are contrasting views within government over the best course of action over TIM, political sources said on Monday. KKR, which consulted Rome before making its offer, plans to carve out the network and give CDP a leading role in overseeing it, sources have said. "A "plan B" in alternative to the current, or an increased, bid by KKR ... could suggest political interference, increased uncertainty ... and further frustration for minority shareholders," said Banca Akros analyst Andrea Devita. Shares in TIM were down 2.4% at 1213 GMT, having dropped 4.4% to 0.444 euros to trigger a trading suspension earlier in the session. Vivendi faces a large capital loss on its 24% TIM stake at the 0.505 euros per share offered by KKR. The U.S. fund has said the price is only indicative and wants access to TIM"s books before making a formal offer. TIM, however, has yet to do so and the special committee it had set up to work on the proposed deal failed to reach a decision over advisers at the weekend. read more ($1 = 0.8863 euros)