The 20-year-old left-back is attracting interest from the Gunners after some impressive performances for Evo-Stick Northern Premier League side Hednesford Town.
According to 'Metro', the full-back, who can also operate as a winger, underwent a trial before Christmas and Arsene Wenger is weighing up the possibility of offering him a deal with the Gunners.
Should the defender join Arsenal, Bramall's rise would be similar to that of Jamie Vardy, who rose from non league to become a Premier League champion.
Here is a glimpse of what Arsenal fans could expect, should they sign Bramall. The non league star sets up a goal with an exquisite rabona cross.