Samir Nasri's family expect the midfielder to stay with Arsenal.
The Frenchman has been linked with Barcelona.
But Dad, Hamid, says: "Samir is just 23, and he has the scope for huge further improvement.
"His game can become even faster. I'm convinced he can reach even greater heights - and that he will do so with Arsenal. They have managed to lift him to the level where he is now."