Vela is again without a club after a short second spell with LA Galaxy, while Sanogo was last seen playing for second-tier side Qingdao Red Lions in China.
Former Arsenal forwards Lucas Perez, Carlos Vela and Yaya Sanogo are all currently without a club.
Despite the transfer window closing last week, Arsenal can still sign players.
There are a number of free agents who can be signed and registered to play in the Premier League, with Arsenal using only 22 of their 25 squad spots.
It follows Gabriel Jesus being ruled out for at least six months with a serious knee injury, and Gabriel Martinelli being sidelined for weeks with a thigh complaint.
