The 31-year-old was almost left out of the final 23-man squad due to the injury and had been expected to miss the June 12 game in Port Elizabeth at the very least.
However, coach Huh Jung-moo has been impressed with Lee's recovery rate and could even pitch him in against the Greeks.
"Lee has made a lot of improvement," Huh told reporters at the team's training base in Rustenburg. "It's possible he could even play a little in our opening game with Greece."
Lee, whose career has been blighted by a succession of injuries, was the K-League's top goal scorer last season but only a lack of striking options saw him make Huh's final 23-man list.
The forward, known as the 'Lion King' at home, was a fresh-faced 19-year-old when he burst into the national squad for the 1998 World Cup.
However, he was left out of the squad for the 2002 tournament on home soil after failing to win over Guus Hiddink and missed the 2006 World Cup finals in Germany after being struck down by a knee injury.
South Korea, who also face Argentina and Nigeria in Group B, are also confident striker Park Chu-young will be fit despite dislocating his shoulder in training in Austria.
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