Son has been in terrific form for Spurs this season, scoring 18 goals in all competitions, but the 25-year-old could soon see his career interrupted.
All able-bodied South Korean males must serve 21 months in the military and Korean law states that the period of service must begin before the age of 27.
However, exemptions are awarded to athletes who win a gold medal at the Asian Games, or an Olympic medal of any colour, and South Korea will be one of the favourites for the football title at the Aug. 18-Sept. 2 Games in Indonesia.
"Son has a strong will to compete at the Asian Games," Yonhap news quoted Kim as saying on his return from Europe on Tuesday. "But first, there's the World Cup. I told Son to play well in Russia before we meet at the Asian Games."
Kim said he had met with Son in Britain as part of his trip to look at candidates for Asian Games selection.
Son, who could be selected as one of three overage wild card, was refused permission by his former club team Bayer Leverkusen to play in the 2014 Asian Games in Incheon when the South beat North Korea in the gold medal match.
Since the Asian Games soccer tournament is not on the official FIFA calendar, clubs are under no obligation to release players but reports in Britain say Spurs are weighing up the possibility of giving Son the chance to earn an exemption.
The 2018/19 English Premier League season is scheduled to kick off on Aug. 11 with the final of the Asian Games football tournament taking place on Sept. 1.
"It's a sensitive issue," Kim said. "I believe the Korea Football Association will handle this matter well. The men's senior national team, the U-23 team, the KFA and the player's club should all work closely."
(Writing by Peter Rutherford; Editing by Sudipto Ganguly)
