Portugese outlet O Jogo, as quoted by the Daily Mirror, is reporting that the north London side are considering making a swoop to sign the 21-year-old this summer.
According to the same report, Arsenal have sent scouts to watch Zivkovic in action for the Portuguese side on several occasions this season as they prepare for the summer transfer window.
The story also says that Manchester United have also sent scouts to watch the winger in action, which could mean a direct bidding war between the two Premier League clubs this summer.
The Benfica star has been in solid form for the Portuguese side so far this season, scoring three goals and making three assists in 14 league games for his club.
Arsenal are bound to be linked with a host of players in the summer transfer window as it provides the Gunners with the chance to significantly bolster their squad.
Meanwhile, Arsenal will take on CSKA Moscow in the Europa League quarter-finals as they bid to try and reach the semi-finals of Europe’s second tier club competition and keep their Champions League qualification hopes alive.
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