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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.