The People says Romeo, 11, and Cruz, nine, are said to be enjoying every minute of honing their skills with the North London giant's youth teams.
The soccer-mad boys love going to watch the Gunners with ex-England hero Becks , 38, but have not signed up with Arsene Wenger's outfit.
A source close to Beckham said: "Romeo and Cruz are with Arsenal and they are enjoying it. The boys are crazy about the game.
"They grew up with it of course and have watched their dad all their lives.
"David is delighted that they like to play. But they are young boys and football is just a hobby. It isn't anything serious at this stage."
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