The Jeonbuk Hyundai Motors forward has been a stand-out for his country in Qatar, becoming the first South Korean to score two goals in a World Cup game in the 3-2 defeat to Ghana, taking his tally to six in 20 caps.
Despite the loss, South Korea progressed through the group stages thanks to a draw with Uruguay and a dramatic injury-time win over Portugal, although their tournament came to an end at the last 16 stage on Monday with favourites Brazil claiming a resounding 4-1 win.
With South Korea now eliminated, the transfer race for Gue-sung is expected to heat up ahead of the January transfer window with Fenerbahce and Rennes also said to be interested, along with Ange Postecoglou’s side.
In a possible boost to Celtic, the 24-year-old’s dad, Cho Chae-hwan, revealed he has advised his son to join a club that will suit his playing style as he confirmed that transfer negotations over a move to Europe are already at an advanced stage.
Speaking to Korean television, Chae-hwan said: "The advice I have given my son is when he signs for a team abroad, go to a club that can play the way he likes, rather than choosing a club because they are a big name. He needs a club that will help him adapt and settle down to a new lifestyle on and off the pitch.
"I know his agent is in the process of finalising negotiations regarding his transfer overseas. He will certainly go to Europe. Ahead of the World Cup, I told him that this was a tournament that he had to show everyone what he could do on the pitch and I think he did that. He has had a great time at the World Cup and I am certainly very proud of him."
Celtic have already added Yuki Kobayashi, the centre-back who can play on the left, from Japanese side Vissel Kobe. His signing was followed by the confirmation that Alistrair Johnston will join up with the team next week after completing a deal from MLS side CF Montreal following his exploits for Canada in Qatar.