Arsenals chief executive Ivan Gazidis spoke with Mikel Arteta in person after Manchester Citys 2-0 victory at the Emirates Stadium on Sunday, according to reports.
Arteta was close to being appointed as Arsene Wengers successor this summer after lengthy talks with Gazidis and Arsenals hierarchy.
But the Gunners opted to appoint Unai Emery instead, primarily because the 46-year-old represented a more experienced option than the former midfielder.
According to the Daily Telegraph, Gazidis is keen to remain on good terms with Arteta and sought out the Spaniard after Arsenals defeat to the Premier League champions.
The report claims that Gazidis was keen to ensure there were no hard feelings between Arteta and Arsenal over the decision to appoint Emery as the manager to replace Wenger.
Gazidis also wished Arteta good luck for the rest of his season with City.
The meeting between the pair was possibly the first time since Arteta held talks over becoming Arsenals manager in May.
Arteta has impressed during his two years as Pep Guardiolas assistant at Manchester City, and the 36-year-old is said to have offered a key piece of tactical advice which led to Bernardo Silvas goal against Arsenal on Sunday.
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