The Manchester City midfielder was, for many, a shock inclusion in Hodgson's provisional 26-man party, having seen first-team opportunities limited during an injury-hit season.
"I've put him on a standby list, which he understands and accepts," Hodgson told reporters.
READ MORE | Rashford set to start for England
"I don't think it's going to be a long-term injury for him, so if I needed him and wanted him to come with us, it's easy for me to call him and ask him to do so.
"But I have actually said to him that, with the situation that we have with the other 25 players, it might be unlikely."
England kick off their Euro 2016 campaign against Russia on June 11.