MILAN, Aug 3 (Reuters) - Telecom Italia (TIM) will finalise the sale of its prized network only if service business finances remain sustainable, the head of Italy's biggest telecoms company told Il Sole 24 Ore newspaper on Thursday.

Debt-laden TIM last month granted U.S. fund KKR an exclusivity period until the end of September to negotiate a binding bid for its landline grid on the back of a preliminary proposal worth 23 billion euros ($25 billion).

The grid sale has encountered strong reservations from TIM's top investor, Vivendi, which is demanding a higher valuation to back a deal and raising concerns over the sustainability of the remaining service business.

With its 24% voting stake, the French media giant could throw a spanner in the works at any TIM shareholder meeting to vote on a deal.

TIM Chief Executive Pietro Labriola also said the group could consider to sell its Brazilian unit "only if huge offer emerges".

($1 = 0.9149 euros) (Reporting by Elvira Poliina Writing by Federica Urso Editing by Gianluca Semeraro and Mark Potter)