MILAN- KKR remains interested in taking over Telecom Italia, the U.S. investment firm said in a letter to the Italian phone group this week, adding it had held "positive exchanges" with Italian authorities on the matter, two people close to the matter said.

In the letter which Telecom Italia (TIM) will examine on Thursday, KKR also said it was open to discussing with the phone group a potential integration of the company's fixed-line assets with those of state-backed rival Open Fiber, the sources said.

KKR has asked to carry out a due diligence analysis of TIM before deciding on whether to proceed with the 10.8 billion euro ($11.9 billion) approach but has narrowed the scope of the information sought, the sources added.

TIM shares traded 9% higher at 1200 GMT at just under 0.33 euros, well short of the 0.505 price per share at which the KKR proposal was pitched.

The former phone monopoly left the New York-based fund waiting for nearly four months without an answer to its approach before its board agreed earlier in March to engage in talks.

While a merger with Open Fiber was not part of KKR's original plans for TIM, the U.S. fund is ready to discuss with TIM the antitrust implications of a such a deal and how it can create value for TIM's unit FiberCop in which KKR is already an investor, the sources said.

A unified ultra-fast broadband network in Italy is the government's goal and will become a reality although there is no certainty on when that will happen, a top economic adviser to the Italian government said on Wednesday.

($1 = 0.9099 euros)

(Reporting by Elvira Pollina; writing by Valentina Za Editing by Keith Weir)