"Christian trained in the week," Hodgson told a news conference. "I don't think it'll be a risk playing him."
Loftus-Cheek, who is on loan from Chelsea, shone in his first England start in last week's friendly against Germany at Wembley but came off injured after the half-hour mark against Brazil four days later.
Hodgson said a back spasm kept the 21-year-old out of training on Thursday but is hoping he will recover in time for the visit of Everton.
Loftus-Cheek has impressed for Palace so far, bringing dynamism and energy to their midfield, and his performances have caught the eye of England manager Gareth Southgate.
Hodgson is already looking forward to a busy January transfer window in which he hopes to address key areas of imbalance in the squad he inherited after Palace sacked Frank de Boer after just four league games in charge.
"There's an obvious gap in our squad," the former England boss said. "We're well-stocked in certain areas, like centre back, but have fewer options in others, like centre forward.
"We have two goalkeepers, other clubs have three, some four. We need to add to the squad."
Everton, who recently parted company with manager Ronald Koeman, are 15th in the table, with three wins, two draws and six defeats so far, but got their first league win under interim boss David Unsworth against Watford in their last match.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
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