The summer arrival from Crystal Palace has battled to live up to expectations in his first season with the Gunners.
And Keown told talkSPORT of Eze's struggles: "I just think this is a case of him actually understanding his role and responsibility in the team.
"So the game against Brentford (1-1 draw which saw him replaced at half-time), I didn't think he was going to press the ball in the same way that (Martin) Odegaard did, and that's a very important thing that you do.
"You keep your opponent at arm's length, if you go and press at source, you stop them coming at you, Eze wasn't doing that.
"(Martin) Odegaard immediately did that when he came on, and then of course, you couldn't get him on the ball.
"You've got to make your mark at a football club, there's no time to lose, and I think he's just making that adaptation, going from Palace to Arsenal."
Keown added: "Once he understands what's involved, the work rate, the energy levels, then I can see a big future for him."