MILAN, June 10 (Reuters) - U.S. fund KKR (KKR.N) strengthened its lead in the race to secure the landline grid of Telecom Italia (TIM) (TLIT.MI) when it offered to raise its bid by up to or over 2 billion euros ($2.2 billion), two people with knowledge of the matter said. The value of KKR's offer could top 23 billion euros overall, widening the gap with a rival proposal by a consortium comprising Italian state lender CDP and Australian fund Macquarie (MQG.AX). The improved offer would still be short of a valuation of more than 30 billion euros for the grid sought by TIM's top shareholder Vivendi (VIV.PA). Sources had previously told Reuters that both Labriola and some leading Italian officials already saw KKR as the strongest bidder prior to Friday's proposal. TIM's board meets to review the proposals on June 19 and is expected to take a decision on June 22.

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Persons: Pietro Labriola's, Labriola, KKR, Macquarie, Akriti Sharma, Elvira Pollina, Marguerita Choy, Leslie Adler Organizations: MILAN, KKR, Telecom Italia, Macquarie, Vivendi, Reuters, TIM, Thomson Locations: ServCo, NetCo, Bengaluru, Milan