Briefing domestic reporters, prosecutors said an anonymous person had contacted the unidentified embassy last week on behalf of Yoo Byung-Eun, 72.
"The embassy rejected the request for asylum as (Yoo) is a criminal suspect," the Yonhap news agency quoted senior prosecutor Kim Hoe-Jong as saying.
It was not immediately clear on what basis the request for asylum had been made.
Yoo is the patriarch of the family behind Chonghaejin Marine Co - the owner and operator of the 6,825-tonne Sewol which capsized and sank on April 16 with the loss of around 300 lives - most of them schoolchildren.
He is wanted for questioning on possible charges of embezzlement and criminal negligence, as prosecutors investigate the extent to which the Sewol disaster was caused by a lack of safety standards and regulatory violations.
Yoo has no direct stake in Chonghaejin, but his children and close aides control it through a complex web of holding companies.
Five Chonghaejin officials have already been arrested.
After Yoo ignored the summons, investigators raided a compound belonging to the Evangelical Baptist Church of Korea, of which Yoo is a leading member, but failed to find him.
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