Perpetual's shares were trading at 31.91 Australian dollars (31.50 US), a drop of 13.8 percent, after discussions with the private equity firm failed to reach "mutually acceptable terms".
"These discussions were aimed at exploring whether a satisfactory offer could be developed that addressed key commercial terms and would be capable of being recommended to Perpetual shareholders," Perpetual said in a statement.
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"However, the parties have agreed that such an offer by KKR cannot be formulated."
Perpetual said it expected to appoint a new CEO soon and reaffirmed its earnings guidance of after-tax profits of 35-40 million Australian dollars over the six months to December.
The 125-year-old financial services group entered talks with KKR after rejecting an initial, non-binding offer of 1.75 billion Australian dollars in October.
