Loftus-Cheek, who is on loan from Chelsea to Palace, has not played since 28th December and there is no sign of an imminent return for the young Englishman.
Palace wish for the 22-year-old to receive surgery, which Chelsea are opposed to as they would prefer for their young star to recover naturally. Loftus-Cheek returned to Chelsea's Cobham training ground last month to undergo treatment at the hands of his parent club, but he is yet to return to training.
The Sun, quoting the Times, reports that Loftus-Cheek is frustrated that his injury could rule him out of selection for England's World Cup squad, suggesting that he may prefer surgery for a faster recovery.
Loftus-Cheek received his first cap for the national team against Germany in November, where he impressed in a 0-0 draw at Wembley. He also started against Brazil four days later, but picked up a knock after 35 minutes and was replaced by Jesse Lingard.
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Crystal Palace manager Roy Hodgson admitted last month that he was being kept in the dark by Chelsea on the subject of Loftus-Cheek's progress.
"Chelsea insist on having him back there on this period of rehabilitation, so we won't really know until such time that they release him back to us," Hodgson said.
Loftus-Cheek made 32 appearances for Chelsea before being loaned to Palace, and scored his first senior goal against Aston Villa in April 2016.