Sanchez, top scorer last season with 24 English Premier League goals in 38 matches, is entering the final year of his contract and has yet to sign a new deal.
"He needs a break," Mertesacker said. "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 what he wants to do. It's his decision. If he feels good, comfortable, he can play with freedom."
Mertesacker is entering the final season of his playing career at Arsenal as he prepares to become the club's academy manager, and the German is eager to finish on a high.
"I want to make the most of it," he said. "I want to stay injury free, be an option for the manager to get picked every weekend. That's the target. To make it as enjoyable as I can. As long as I am here I want to play and contribute."
Meanwhile, Manchester United captain Michael Carrick said striker Romelu Lukaku must be ready for a big adjustment after joining from Everton.
The 24-year-old Belgian made his debut in a 5-2 friendly win over LA Galaxy last weekend, and Carrick expects Lukaku to thrive in an environment where expectations are high.
"The jump is massive," Carrick said. "I found that myself coming from Tottenham. But having Premier League experience is a massive bonus. He'll know how things work week to week. It's just about dealing with pressure.
"It's early days. It's one week's training and 45 minutes against Galaxy. So you can't come to any conclusions. We know what he's about.
"Obviously, he's been brought here to score goals. I am pretty certain he'll do that."