The highly-rated 19-year-old came off the bench against Dundalk in the Europa League win on Thursday to make his Arsenal debut.
Arteta said, "Obviously I've got this situation and I believe it's later than what I would like because I wasn't here when everything started to develop but yes, he's a player that I would like to give chances to.
"That's why he was in the squad today and I showed him that yes, we count on him and we believe in him and if he wants, he's going to have a future in the club."
The American-born forward netted 25 times in just 19 appearances when playing for Arsenal's under-18 side.
Sheffield United were one of the teams interested in snapping Balogun up during the transfer window, bidding £3million for his services.