Johnson played for both clubs during his career.
"Yes. Possibly. West Ham's a fantastic football club and they will let Alex enjoy his football," he told BettingOdds.com.
"Obviously the only concern with Ox is that he's got to stay fit, because he's a fantastic player with bags of energy and great ability but that's no good on the treatment table.
"Hopefully his body can get through all of next season. But I think West Ham United and Oxlade-Chamberlain would be a perfect fit.
"Moyes would take the shackles off him, let him go and enjoy himself, and see what he can do. Touch wood Alex can stay fit and get back to his best."
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