The Swiss international spent just a season in Turkey with parent club Galatasaray following his move from Napoli last summer.
“I really wanted to go back to Italy,” Dzemaili told Sky Sport Italia.
“Last season started well for me but ended badly because of my injury.
“I want to say thanks to Genoa for the opportunity they have given me and to the president for making it happen.
“Playing with Pandev again? By now I think we will end our careers together … (laughs). Seriously we are very good friends.”
Before he moved to Turkey the 29-year-old spent three seasons with the Partenopei making 86 Serie A appearances and scoring 16 goals.
