In a statement on six-month results, Italy's biggest phone group, whose largest shareholder is French media group Vivendi, said it had examined the financial implications of taking part in 5G auctions Italy is launching later this year.
"(The group) has started an evaluation process of the strategic options relating to its subsidiaries," it said.
Besides Persidera, it did not mention specific subsidiaries but TIM Chief Executive Amos Genish has said in the past submarine network unit Sparkle is not core.
TIM said its earnings before interest, tax, depreciation and amortisation (EBITDA) in the first six months fell 4.8 percent to 3.92 billion euros (3.49 billion pounds)while sales fell 2.7 percent to 9.51 billion euros.
Both results were in line with an analyst consensus provided by the company.
In May Genish said towers unit INWIT remained strategic while its business in Brazil was not for sale.
Activist fund Elliott wrestled TIM board control from Vivendi in May after a two-month campaign to shake up the way the French group has been running the former telecoms monopoly.
Elliott has proposed asset sales at the group as well as a series of other measures including governance overhaul, a spin-off and partial sale of the company's soon-to-be-created network company, and a conversion of savings shares.
Genish is looking to execute a three-year plan launched in March focusing on a digital transformation of the group, fixing its finances and getting back investment grade credit rating.
A major headache is the arrival in Italy of French rival Iliad which in May presented its new low-price mobile offer in the country.
TIM, which made no reference to its financial outlook for the full year, is due to hold a conference call on the results on Wednesday.
($1 = 0.8561 euros)
(Reporting by Stephen Jewkes; Editing by Adrian Croft)
By Stephen Jewkes