Arsene Wenger has been sending scouts to watch the French international defensive midfielder.
Gonalons, 24, who has three years left on his deal, is once again set to be watched by Arsenal in Lyon’s trip to Nancy on Sunday.
Wenger is desperate to bag a holding midfielder this summer after losing Abou Diaby for the rest of the year with a knee ligament injury.
Gonalons, a Lyon player all his career, boasts a reputation for being extremely consistent.
Wenger has £70m to spend this summer and is also looking to buy a striker, goalkeeper and central defender.The Gunners remain hopeful of landing Fiorentina hitman Stevan Jovetic.
The clubs started talks last week. They have yet to agree a fee but it seems likely they will strike a deal, with Montenegro star Jovetic, 23, desperate to move to the Emirates.