The Sun is reporting that the north London side watched the 21-year-old winger in action for the Portuguese club against Maritimo with a view to making a possible summer bid for the attacker.
The same story says that both Arsenal and Manchester United are keen on signing the young attacker ahead of the summer transfer window.
The Serbia international helped his club win a Portuguese league and cup double last season and Arsene Wenger is reported to have asked Arsenal scouts to keep tabs on his progress since then.
The same article says that Zivkovic is under contract at Benfica until 2021 and that his current employers value him at around £6.3m.
Both Arsenal and Manchester United are likely to be keen to bolster their squads in the summer transfer window as both team look to try and challenge Manchester City’s Premier League dominance next season.
Zivkovic has scored three goals and made three assists in 12 league games for Benfica so far this season. He has also made one assist in the Champions League for the Portuguese side.
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