Arnautovic quickly endeared himself to the Britannia faithful during his cameo debut against Manchester City on Saturday.
"It would be brilliant if we could replace the great man," Coates told The Sentinel. "If he can take his place we will be more than pleased.
"There is every reason to suppose our crowd will enjoy him and warm to him. "He certainly looked a confident player to me and we know he is a talented one.
"But we must also remember this is a new situation for him. A new team, a new league and a new country, so it is only fair we are patient and give him time to adapt to his new environment."
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