Loftus-Cheek spent the last campaign on loan at Selhurst Park, and a return of two goals and three assists from 24 outings earned the 22-year-old a place in England's World Cup squad.
Chelsea are yet to decide whether the playmaker will remain at Stamford Bridge this season, and Hodgson has suggested that he is keeping an eye on developments in West London.
The Eagles boss told talkSPORT: "We'd love to have him back. There is no question about that but that is something which is totally and utterly in Chelsea's hands.
"I have no idea what their plans for Ruben are. They haven't announced to us what their plans are and I've seen nothing written publicly but Ruben knows how much we appreciate him and how pleased we were with him, and the fans took him very much.
"If he was available on loan, I am pretty sure we would be knocking their door down to get him."