The Magpies held talks with the 26-year-old, who is out of contract with Japanese J-League club Shimizu S-Pulse, but have decided against a deal in the January transfer window.
A club spokesman said: "The club has had discussions with the player and his representatives, but has decided not to proceed."
Cho, who has scored eight times in 29 senior international appearances, is being courted by five Premier League clubs, according to agent Kim Min-jae, with Fulham and West Ham among those to have been linked with him in recent days.