On 23 August 2015, in the opening match of the 2015–16 Serie A season, Kone, as a substitute, helped Udinese stop Juventus' 47-game unbeaten streak at home in the league by providing an assist to teammate Cyril Théréau in an eventual 0–1 away win. On 13 October 2015, Udinese confirmed that Kone suffered a calf injury while on international duty with Greece and would be out of action for two-and-a-half months. On 17 December 2015, Kone made his return to the team, scoring an impressive goal against Lazio in the 2015–16 Coppa Italia; controlling a cross with his heel, he swung his leg around and acrobatically flicked the ball into the top-left hand corner of the goal. Despite the individual effort, however, Lazio prevailed 2–1, knocking Udinese out of the tournament. On 24 January 2016, Kone almost 4 months since his last appearance with the club in Serie A, played again as a substitute for Emmanuel Agyemang-Badu in a 4–1 away loss against Palermo.