Battling an embarrassing scandal in which 10 players have been arrested for alleged involvement in match-fixing, K-League officials have yet to decide when the window will close.
"The deadline was set for today, but team representatives have agreed to extend it," the K-League told South Korea's Yonhap news agency.
"We promised to keep all related information confidential, so we can't say how many players have approached us. It's still inadequate, but it's progress."
The K-League's match-fixing probe has so far caught 10 active players along with gambling brokers, with those found guilty facing life-time bans and up to seven years in jail.
The players caught so far have been charged with taking money in exchange for helping their teams lose two matches in April, prosecutors said.
Eight of them are from the Daejeon Citizen team, with one player accused of receiving 120 million won ($110,600) and also sharing it with seven team mates.
A player was also found dead last month in a hotel room, with Yonhap reporting a suicide note had been discovered referring to the match-fixing ring.
The league has ordered players to report their involvement in return for reduced punishments for those who turn themselves in.
State-run sports bookmaker Sports Toto has stopped taking bets on games at the request of K-League club owners, while the government has threatened to terminate funding for sports leagues tainted by match-fixing.
