KKR's approach incorporates a value for TIM's fixed landline network that could top 23 billion euros ($25 billion).
TIM plans to analyse in depth the terms to be proposed by KKR, one of the sources said.
Having already invested 1.8 billion euros in the grid, KKR has bid for a controlling stake in a unit comprising TIM's entire domestic fixed access network and submarine cable business Sparkle.
KKR is also ready to let TIM retain a stake in its landline network.
Prime Minister Giorgia Meloni's administration will have a say on any deal as Rome can use its "golden powers" rules to set conditions or block bids for strategic assets such as TIM's network.
Persons:
Pietro Labriola's, Giancarlo Giorgetti, Giorgia Meloni's, Giuseppe Fonte, Elvira Pollina, Valentina Za, Kirsten Donovan
Organizations:
KKR, TIM, Telecom Italia, Macquarie, Reuters, Vivendi, Treasury, Thomson
Locations:
ROME, Rome