Terry had been expected to leave Chelsea this summer but the 35-year-old accepted new manager Antonio Conte’s offer of a one-year contract last month.
Desailly, who left Chelsea in 2004 after six seasons in west London, mentored Terry when he became a first-team regular in 2000 and the pair are still on good terms.
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Desailly, speaking in Paris at an event to mark Danish brewing giant Carlsberg’s sponsorship of Euro 2016, told Press Association Sport: “He is still the leader and maybe Conte met him and realised that John is still ready to sacrifice everything for the club.
“John doesn’t have to be first choice but keeping him is good for the continuity of the team.