Palace are now seeking a new manager after Oliver Glasner announced he would be leaving at the end of the season when his contract expires.
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TalkSPORT says Keane is a top target for the Palace board, with the Irishman impressing with Hungary's Ferencvaros, having previously led Maccabi Tel Aviv to the title in Israel.
In addition, he has also been an assistant trainer for Ireland, Middlesbrough and Leeds.
Removing Glasner and installing Keane before the end of the season hasn't been ruled out by Palace management.