Arsene Wenger has reportedly suggested his replacement.
The Frenchman’s contract is not due to expire until the summer of 2019.
However, it is suggested that Wenger has assisted the hierarchy by outlining van Bronckhorst and Bournemouth boss Eddie Howe as possible successors.
Van Bronckhorst currently manages Netherlands outfit Feyenoord, who are seventh in the Eredivisie.
The 42-year-old did lead his side to the league title last season and won the domestic cup the previous year.
According to the Daily Star, Wenger thinks van Bronckhorst would be just the man to guide the Gunners forward.