Loftus-Cheek, 21, was also thought to be a target for Newcastle United, but instead could opt for Selhurst Park on this expected season-long loan.
Frank De Boer would add his first player since being hired by Palace.
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Loftus-Cheek has 32 appearances for Chelsea with two goals, one of those being a marker in the Premier League two seasons ago. He made just 11 total appearances for Antonio Conte last season, and did not score a goal.