Arsenal have won only four of 13 games in all competitions since the start of December.
But Coquelin, who insisted there was “no crisis" at Arsenal, told the BBC World Service: “People tend to forget what Wenger has done for the club. I understand the frustration but everyone should stand by him, everyone should be behind [him].
“That's the only way results are going to turn around."
"If they let Sanchez go, what I am sure of is they will have to strengthen the team, because he will be a big miss," Coquelin added.
“For fans, they demand a competitive team. They will be upset if no-one comes in the transfer market and they let Sanchez go."