In the 2019-20 Serie A season, the Frenchman contributed seven assists and three goals to his team.
In an exclusive interview with Gazzetta dello Sport, Fofana said it is time for a new experience.
“My cycle in Udine ends here after four beautiful years,” said Fofana. “I have to think about myself. The time has come to choose another destination.”
Whether that destination will be in Italy or abroad remains to be seen.
Fofana added: “I am a nomad. I have played in three countries, Italy, France and England.
“I never thought I’d come to Italy but I’ve stayed here for four years and maybe I’ll remain here. But it’ll be difficult to find somewhere I’ll be as happy as Udine.
“I’ve played for Fulham and Bastia, but Udinese feels more like Manchester City. My choice [of a new club] will be a sporting, not financial one.”
Fofana is under contract with Udinese until June 2022 and has a current market value of €9.5m.
A former France under-21 international, Fofana opted to represent Ivory Coast at senior level and has won four caps.