The seven include three from Nepal, two from Sri Lanka and one each from Bangladesh and Palestine.
"We've planted informants in areas where many workers from these countries live" to collect information about missing athletes' whereabouts, a senior police official told AFP.
Most Asian immigrant workers reside in satellite cities around the capital Seoul such as Incheon, Bucheon and Ansan.
"When we find them, we will ask them to leave the country even before their visa expires on October 19 as they left the athletes' village without permission", the official said.
Sixteen athletes from those regions vanished during the 2002 Busan Asian Games.
Every year South Korea issues visas for tens of thousands of foreign workers from Vietnam, the Philippines and other Asian countries to help ease manpower shortages.
More than 200,000 foreign workers are also illegally employed in manufacturing, construction and other industries.
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