Antonio Conte has completed the £15 million capture of one England international midfielder.
That deal could edge another Three Lions star through the exits, with Loftus-Cheek having been loaned out amid fierce competition for places.
The 21-year-old has found regular game time at Palace, allowing him to force his way into the senior international fold, and Hodgson admits he will be asking questions of Chelsea during the January transfer window.
He told reporters on Loftus-Cheek's future: "He's a player we'd like to have at our club, there's no doubt about that.
"Ruben's a player we like very much. We're very impressed with him, delighted with the way he's developed as a player during the time he's been here. I'm pretty sure that if he's ever available for sale, we would certainly be in there with our hand up as one of the potential buyers.
"It could well be that Chelsea would like to have both Ross Barkley and Ruben Loftus-Cheek in their team. I wouldn't mind both in my team, anyway.
"I didn't know until this morning that Ross Barkley is possibly signing for Chelsea."
While being open to discussing one deal during the winter window, Hodgson has reiterated that no talks will be entered into regarding the possible sale of Wilfried Zaha.
Hodgson added: "People who make offers for Wilfried Zaha are basically wasting their time.
"I'm certainly not expecting it. I have it on very clear authority from the chairman and owners of the club that they have no interest in selling Wilfried Zaha: quite the opposite.
"Our job is to keep all of the players we've got, who've been doing reasonably well for us in the past few weeks, to keep all of them, keep them fit, and add to it, and make ourselves stronger.
"I would advise people thinking of making offers to save it, because they're going to be turned away, and might just be wasting the price of a phone call."