"The injury is more severe than we originally thought, or perhaps hoped, it would be," Hodgson told reporters on Thursday.
"I would be very disappointed, surgery or no surgery, if he's not playing before the end of the season. We certainly want him to be and I would presume Chelsea would want him to be.
"The only way he can make himself available for Crystal Palace or England is to be fit and at the moment that isn't the case."
Loftus-Cheek made an impressive start to his season-long loan stay at Palace, earning himself an England debut against Germany at Wembley last November, followed by a second cap in the next match against Brazil.
Asked whether Loftus-Cheek was a doubt for the World Cup, which kicks off on June 14, Hodgson replied: "I don't know. I don't want to go into that at the moment because we don't know how long it would take after surgery to get him fit again."
Palace, currently 12th in the Premier League standings, visit sixth-placed Arsenal on Saturday.
(Reporting by Hardik Vyas in Bengaluru; editing by Amlan Chakraborty)
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