The 29-year-old is currently a free agent after running down his contract at Portuguese side Porto.
But it is understood that personal terms on a switch to the Emirates Stadium are still a way from being agreed.
Brahimi enjoyed the best goalscoring campaign of his career to date last season, netting 13 goals in 49 appearances as Porto finished second behind champions Benfica.
The Algeria international joined Porto from Spanish side Granada in 2014 and has since scored 53 goals in 209 matches.
Yacine Brahimi in action for Porto
Brahimi scored 13 goals for Porto last season.
Brahimi, who helped Porto win the Portuguese title in 2017/18, attracted interest from West Ham last summer.
Arsenal boss Unai Emery is keen to strengthen his attacking options and is also expected to launch a bid for Crystal Palace forward Wilfried Zaha.
It is understood Zaha wants to stay in London and play European football next season.