Sanchez has less than a year left on his current Gunners contract and has so far shown no obvious desire to sign a new one, particularly now after expressing how important Champions League football is to him, something Arsenal cannot offer.
If he isn't sold this summer, the Chilean could walk away as a free agent next year, and both Paris Saint-Germain and Manchester City are believed to be keen to buy him right now.
In the event he does leave, Don Balon say the Benzema pursuit that has so frustrated fans in recent years will be back on. Their report even labels the player a 'great obsession' of Arsene Wenger.
Benzema had something of a down season at Real in 2016/17, scoring fewer than 20 goals in all competitions for the first time since his debut season at the Bernabeu as a youngster in 2009/10. With Alvaro Morata desperate for his chance after losing the opportunity to lead the line at Manchester United, it's feasible the Frenchman could now come under pressure.
It remains to be seen how much truth there is to it, but with Arsenal already having landed £46m Alexandre Lacazette this summer, any Benzema pursuit would have to hinge on Sanchez.
Fortunately or unfortunately, depending on which side of the highly divisive Sanchez fence you're on, Arsenal are determined to keep hold of the Chilean contract rebel for this season, regardless of the risk he becomes a free agent in 2018.
"The decision has been made and we will stick to that. The decision is not to sell," were Wenger's defiant words on the matter at a press conference earlier this week.