The Chile international's future has been up in the air for a number of months due to his reluctance to sign a new contract at the Emirates Stadium.
Sanchez is due to see his current deal expire in a year's time, meaning that the Gunners may be forced to cash in if they do not want to lose him for free next summer.
Further doubt was cast on the forward's Arsenal future on Saturday when he gave his biggest hint yet that he wants to leave, but Mertesacker believes that his teammate simply needs time to clear his head before committing.
"I am very confident [he will stay]," he told reporters. "It's his decision. If he feels good, comfortable, he can play with freedom. He has his qualities. You cannot find those everywhere.
"I have not spoken to him. He needs a break now. He needs to relax. He has done a lot for us. He played almost every game last season and then the Confederations Cup.
"You need to leave him alone to make up his mind about what he wants to do. He has one more year here and then he makes his mind up. It's his decision."