Zenga took charge at the club in April 2009 and has managed to secure their top flight status both seasons.
“I am finished with this period at Catania,” he told Sky Italia.
“The last 14 months have been really good but I want to leave now in a positive manner, with a good relationship with the club. I have no regrets about this decision.
“Where will I go? Anywhere. I am a loyal person and if I say I have had no contact with any other team, that is true.
“I’m without a side for next season, but I’m not worried. I don’t know what I will do, but let’s wait and see what happens.”