The 48-year-old was widely expected to lose his job at the end of last season, with the Blues finishing fifth in the Premier League table.
On Thursday, multiple media reports claimed that Conte was no longer Chelsea manager, though the club has yet to confirm the news.
Terry, who played his last season at Chelsea under Conte en route to the 2016-17 Premier League title, paid tribute to his former manager on Instagram.
"Love this man," wrote the former England defender. "Thanks for everything Boss.
"In a time that should have been the most difficult season of my career, Antonio was honest, respectful and there for me whenever I needed him. I loved working and learning from him."
Former Napoli coach Maurizio Sarri is widely expected to take the reins at the West London club.