Pulis has long been linked with the available job as Palace boss and is reportedly in advanced talks with the club board.
Palace has been without a manager since Ian Holloway stepped down last month.
Pulis has been out of work since his second spell at Stoke ended in May.
The 55-year-old has never been relegated as a manager.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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