That is according to former scout Goran Milosavljevic, who was speaking in an exclusive interview with Tribalfootball.
Milosavljevic worked indirectly with Arsenal as a scout in the Balkans for 15 years before Wenger's departure last season.
However, Wenger decided against pursuing the Serbian midfielder, who eventually joined Marseille this summer.
"Its difficult to find quality and personality in a player. Arsene Wenger was very careful about personality. I think all coaches need to look at personality as well as quality," Milosavljevic told Tribalfootball.
"He [has] moved now to Marseille in France. This is [Nemanja] Radonjic and I spoke with Arsene about his quality, enough for [the] English Premier League. And Arsene listened to me for maybe 10 minutes and first question he said, 'Goran, how is [his] head? [Does he] have a good head?'
"Before he had problems but he came back because he has many agents around him and he work a lot on his psychology. Arsene looked immediately at his personality."
Radojnic, 22, failed to make a first-team appearance for Roma after graduating from the club's academy in 2014.
And Milosavljevic believes Radojnic earned the move because current Marseille boss Rudi Garcia worked with him at Roma and was able to recognise his development.
He added: "Now this player goes to Marseille because Rudi Garcia knew the boy from AS Roma and I think he saw his progression in his personality outside the stadium."
Radojnic has made one appearance for his new club so far this season.