Parker was captain in Stuart Pearce's temporary reign but the 31-year-old lost the armband to Steven Gerrard, on Wednesday.
Hodgson said: "Scott's had an injection which will probably take a week for us to see if it's been successful or not.
"He could still miss out, although from what I'm hearing, it won't be a problem. He's very confident."
The manager added: "We've got until the 29 May to finalise the squad and I may still have a call to make on that one if it's looking dubious, if there is a doubt.
"I'll have that call to make. Do I take the risk and go with a doubt and hope for the best or do I say 'I'm sorry, I've selected you in my 23 players, but now I have to remove you'?
"But I'm very confident that won't happen. I'm very optimistic. The doctor spoke to Scott Parker and Spurs on Wednesday, so I'm confident - but I can't give a guarantee."