Campbell steered the Gunners to two Premier League titles and three FA Cup crowns after jumping ship from Spurs in 2001.
Though Arsenal have found roles in the past for legends of the club, Campbell concedes the club haven't responded to him about doing his coaching badges with them.
"I asked if I could do some of my badges there and I've had a few texts, but they've not got back to me with a firm offer to return. I'm disappointed.
"I talked to the other coaches and they're fine, but I went out to Andries Jonker [Arsenal academy coach] and he hasn't got back to me. Is it rude? I don't know.
"He's the head guy, the other coaches are fine but he's the head guy and I've got to go through him to make sure I don't tread on anyone toes but I haven't heard back.
"I'm talking about going to Arsenal once or twice a week for a couple of hours just to learn a bit about a coaching role - that's all - but I've heard nothing."