Llorente signed for Tottenham in the final days of the summer market, but only after Chelsea had failed with a nominal €5.5m offer for the Spain international.
Conte wanted to add Llorente to his squad, having tried for the veteran in January. The pair worked together at Juventus.
Llorente said at the time: "The truth is that Chelsea has been following me for a while, but in the end you know how it works. At the last minute of the transfer window, (Mauricio) Pochettino called me and convinced me to join Tottenham."
After venting, Conte eventually climbed down and agreed to stay with Chelsea with the season already underway.