The winger is in demand, with Milan, Roma and Atletico Madrid all reportedly interested in securing his services, but Cairo is eager to keep hold of him.
However, the president does not want to retain a player against his will, so would listen to offers if the 27-year-old does want out.
"Yes I have said that I want to keep him, but also [it is important] that he wants to stay," Cairo told TorinoGranata.it.
"I want very much for him to stay with us, we are fond of him and he is a great player. But equally I hold to the fact that he is persuaded to stay."
Cairo, when asked whether the club had received any offers for Cerci, responded: "These are things we will keep confidential. Evidently, the player is liked.
"He has just returned and I have not seen him yet nor even welcomed him. Let's say that we have not decided on any reasoning. I repeat, he has just returned, we have not yet seen him and I want to hear and talk to him and then we will work out our approach to the case."
Cerci, who scored 13 goals in 37 Serie A appearances last season, was part of the Italy squad that exited the World Cup at the group stage.