Krieviņš said that none of the applicants fit the competition criteria. A new competition will be announced and further action is expected "as soon as possible".
He said that if the competition is delayed, an acting head will be taking over the office.
Previously Krieviņš told Latvian Radio that the competition committee is expected to produce a decision by November 10.
As reported, the current Corruption Prevention Bureau head Jaroslavs Strelcenoks' term in office ends November 17.
Strelcenoks was among the four people who had confirmed their candidacy, meaning that his bid for reinstatement has been turned down.
KNAB's remit to fight corruption has been repeatedly hampered for a decade by attempts at political interference, internal dissent and dissatisfaction with its leadership.