Arena told The Sun: “As a trainer or a coach, he is improving.
“He works hard, he's well liked, he's articulate, he's got all the qualities and a player of that background, a product of Arsenal Football Club is certainly someone they are going to consider.
“Some would say that about Thierry Henry as well, but Patrick Vieira has a stronger coaching background right now."
Arena says the former midfielder's career has influenced his approach to tactics, comparing New York's style to that of Pep Guardiola's City.
He said: “I think his training at Man City and obviously Arsenal, it's a blend of both of those styles.
“It's an attack-orientated team. It's a collaboration of efforts. No one individual is more important than anyone else."