The Gunners finished a disappointing eighth in the Premier League last season, leaving them without European football.
Arteta has moved quickly to revitalise his squad by signing Nuno Tavares and Albert Sambi.
But the Spaniard still wants to sign a central midfielder, creative midfielder, goalkeeper and a right-back this summer, per football.london.
Houssem Aouar and James Maddison have been touted for the midfield roles.
Hector Bellerin has asked to leave the club, and Arteta must now find another right-back.