The north London club are keen to get their transfer business done early this summer and have already secured both Alexandre Lacazette and Sead Kolasinac.
They are now keen to land Eintracht Frankfurt's teen ace Barkok.
Arsenal have reportedly been monitoring the 19-year-old throughout his debut Bundesliga season, during which he played 18 times and scored twice from his midfield.
According to reports, an initial offer from Arsenal which was below £10m has been snubbed by the German club.
But it has been suggested that Frankfurt are bracing themselves for another approach for Barkok, who is currently away with Germany's Under-19 side.