KKR has made a 10.8 billion euro ($12 billion) offer in the midst of a boardroom row between Gubitosi and the former Italian telecoms monopoly's top investor Vivendi.
Gubitosi said in a letter sent to the board on Thursday that it was time to take action, appoint advisers and make a decision on KKR's offer, the sources told Reuters, confirming an earlier report by Italian news agency Ansa.
"Time-wasting attitudes by the board that could be interpreted as aimed at defending the interests of certain shareholders are to be avoided," Gubitosi said in the letter.
"Technically we could be ready for a data room in 48-72 hours," he said in the letter, referring to the practice of giving a suitor and its advisers access to a company's books to conduct due diligence during a potential bid.
French media group Vivendi has been pushing for a change at the helm of Italy's biggest telecoms company.
Gubitosi's comments came as auditors and the risk committee at TIM examined the group's financial health after two profit warnings since July which have strengthened Vivendi's hand in demanding a change at the helm.
Vivendi declined to comment.
($1 = 0.8913 euros)
(Reporting by Elvira Pollina and Agnieszka Flak ; Editing by Alexander Smith, Kirsten Donovan)
By Elvira Pollina and Agnieszka Flak