Thomas Partey and Houssem Aouar were both linked with a move to the Emirates with the Ghanaian eventually making the switch on deadline day.
Arsenal paid the release clause to sign Partey from Atletico Madrid with it being claimed that Edu got his way.
French outlet L’Equipe claim Edu’s word had more weight than Arteta’s, with the Spaniard preferring Aouar instead.
The report adds that Lyon are delighted to have kept hold of Aouar and Memphis Depay this summer with both having been linked with moves away.
Partey made his first Premier League start for Arsenal in the defeat to Leicester with Arteta having previously praised the midfielder.
Upon confirming the signing, Arteta had said: "We identified him a few months ago and we have been following his progress, and obviously the more you know about the squad, you know more about where you think you can improve it.
"We believe he has the right qualities, with his character and his personality and as well with his technical qualities and positional options that he can give to the team.
"I think he allows us to play different formations and he can fit in within those formations in different positions, which is a really good thing to have in a squad where, in midfield, I think we were a little bit short.
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"I have a few things in mind that I want to start to train with the team and [Partey's signing] is going to give us a little bit more adaptability and more balance in defending and attacking transitions and the way we have to set up certain structures to attack better in certain moments of the game."