Julian Winter resigned as CEO of the Magpies earlier this month after less than six months at the club, subsequently linking up with Championship side Huddersfield Town.
According to the Nottingham Post, Turner - who stepped down as chief executive of Newport County in January - will take his place.
Turner has been involved in football for more than 20 years at a variety of clubs including Bath City, Cardiff City, Plymouth Argyle and Newport.
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