KKR made a 10.8 billion euro ($12.2 billion) offer for TIM last month, just before a boardroom row forced group CEO Luigi Gubitosi to step down following a clash with top investor Vivendi after two profit warnings since July.
Last week, TIM placed oversight of the group's strategic assets in the hands of Chairman Salvatore Rossi, setting up a special committee to study the KKR bid.
Unions have expressed concerns over the future of TIM's 42,500 workers across Italy and have told the company they will not accept any reorganisation that puts jobs at risk, a document seen by Reuters shows.
"We want to be involved in any decision concerning an overhaul of the group," Riccardo Saccone of the SLC-Cgil union said, adding a strike at TIM could be called within 10 days.
TIM was not immediately available for comment.
Any takeover deal is conditional on support from TIM's board and the Italian government, as well as due diligence expected to last four weeks.
TIM's fixed network is Italy's main telecoms infrastructure and Rome has said its response to KKR will hinge on plans for the network which it sees as strategic. State lender Cassa Depositi e Prestiti is TIM's second-biggest shareholder.
($1 = 0.8827 euros)
(Reporting by Elvira Pollina; Editing by Mark Potter)