In a thinly-veiled attack on current coach Juergen Klinsmann's selections, Arena said he wanted to see more American-born players in the squad.
"Players on the national team should be - and this is my own feeling - they should be Americans," Arena told ESPN's The Magazine.
"If they're all born in other countries, I don't think we can say we are making progress."
Since taking charge of the US team in 2011, Klinsmann, a World Cup winner with Germany in 1990, has picked several players that were born and raised in his native country but are eligible to play for the US because they have an American parent.
The squad for Friday's World Cup qualifier against Costa Rica includes two German-born players.
Midfielder Jermaine Jones was born in Frankfurt and played three internationals for his homeland before switching allegiance to his father's country of birth.
Striker Terrence Boyd was born in Bremen and currently plays for Austrian club Rapid Vienna.
Full-backs Timmy Chandler and Fabian Johnson and midfielder Danny Williams, all German born and playing in the Bundesliga, would almost certainly have been called up for this month's qualifiers had they not been suffering injuries and illness.
"I don't even know some of the players, which is odd as the former coach," said Arena.
Arena coached the US at two World Cups. In 2002, his 23-man squad included five-foreign born players. In 2006, there was just one overseas-born player.
Arena's comments followed a report by the Sporting News on Tuesday where an unnamed member of the national team squad questioned whether the German-born players cared enough about the team.
Arena, who coaches the Major League Soccer champions Los Angeles Galaxy, said he wanted more players from the domestic competition picked, but denied taking a free shot at Klinsmann's performance as coach.
"That's not for me to state publicly. I think his goal is to get his team to the World Cup, and I think they'll do that," Arena said.
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