Conti said in a statement on Thursday he was considering the move "in light of the renewed climate of trust and collaboration within the board and between the shareholders," confirming press reports that he was planning to quit.
Conti was appointed chairman of Telecom Italia in May 2018 by U.S. activist fund Elliott, which controls two thirds of the 15-strong board.
He soon became embroiled in a dispute with French media group Vivendi, TIM's top investor with a 24 percent stake, which has accused him of favouring Elliott as the two sides engaged in a protracted boardroom battle.
A source with knowledge of the matter said Conti's resignation could be announced at a TIM board meeting scheduled for Sept. 26.
A separate source had earlier said Conti's exit would be a step forward towards a broader deal between the company's leading shareholders, which include state holding Cassa Depositi e Prestiti (CDP) with a 10 percent stake, over governance at the group.
A third source said that TIM Chief Executive Luigi Gubitosi could take on the chairman role on an interim basis while the company looks for a permanent replacement.
News that Conti was planning to resign was first reported by la Repubblica daily on Thursday.
Longer term, a truce between Vivendi and Elliott is expected to help the creation of a single network operator, a project backed by CDP which, however, has been one of the main bones of contention between Elliott and Vivendi.
(Additional reporting by Stefano Bernabei in Rome; Editing by Alistair Bell)
By Elvira Pollina