Gomez, 22, currently plays for Stuttgart and is making a huge name for himself in the Bundesliga. Last year he was voted the German player of the year and this season he is currently the second highest top scorer in the Bundesliga, behind Luca Toni, having scored 18 goals in 23 appearances.
His goals have brought him to the attention of Wenger and the young striker is thought to be interesting the Arsenal manager who is looking to bolster his strike force.
Gomez, who despite the Spanish sounding name - his father is Spanish but his mother German, has already broken into the German national side.
The striker will be looking to make an impact this summer at Euro 2008 and if he does, no doubt his price tag will rocket.