'It wasn't easy for me to convince you in the beginning but in the end I hope I did you proud!
Blues legend John Terry also sent a message to Conte, who he played under in his final season at Stamford Bridge.
Indeed, Napoli chairman Aurelio De Laurentiis confirmed earlier this week that an agreement was Chelsea was close, in a deal that would also see Italian worldwide midfielder Jorginho move to Stamford Bridge for around €57m.
City have not given up on the player, having reached an agreement on personal terms with him two weeks ago, although there is a fear Jorginho could have become a pawn in the Sarri situation.
Despite Napoli acquiring Carlo Ancelotti, Sarri's contract hasn't been terminated by the club and this has what delayed Chelsea's move.
However, while present players may have had issues with Conte, former Chelsea legend John Terry, who left after the league title-winning campaign had nothing but praise for him.
However, they finished fifth in the 2017/18 season, missing out on a place in the Champions League and consequently costing Conte is job.
If the reports prove to be true, Chelsea would be looking for a 13th permanent boss of Roman Abramovich's ownership, which began in June 2003.
Conte still has one more year running on his current contract and wants Chelsea to pay all of his £9m clause in full.
De Laurentiis was quoted as saying: "Sarri is close to being new Chelsea manager".
Meanwhile, Italy midfielder Jorginho looks set to move to Stamford Bridge along with Sarri.