Despite speculation linking him with a move away after a season in which he was the target of considerable criticism, the Germany international is expected to sign a new contract with Arsene Wenger's side.
But on talk of a possible return to Gelsenkirchen, Ozil told the Funke Media Group: "Right now, I'm not thinking about it. But in football you cannot rule out anything.
"My family would be very happy about a return.
"Schalke is my absolute favourite club, I'm still a big fan. After all, I grew up with Schalke.
"They have wonderful fans and a great stadium. It is a pity that they are stuck in mediocrity. This fantastic club deserves more."
Schalke finished 10th in the Bundesliga during the 2016-17 campaign.