Borussia Dortmund are hoping to sign the Germany-born youngster, as first team opportunities appear limited for the USA U-20 international.
Zelalem, who was born in Berlin, has declared to play for the United States, the birthplace of his parents.
The midfielder was tipped for a big future at Arsenal, but has failed to live up to his early potential and has made just four first team appearances for the Gunners.
The 19-year-old spent last season on loan at then Scottish Championship side Rangers and made a total of 28 appearances for the Scottish Giants.
Borussia Dortmund are hoping that they can persuade the midfielder to return to his country of birth and hopefully live up to his expected potential.