The Tottenham midfielder has been struggling with an Achilles tendon injury that forced him to miss the last four games of the season, and is a doubt for the European Championships
The tireless worker has seen to become an integral part of the England team over the past few seasons but could be a huge miss as the tournament edges closer. England boss Hodgson does not know if he has Parker available yet but seems optimistic.
"Scott's had an injection which will probably take a week for us to see if it's been successful or not," Hodgson told reporters.
"He could still miss out, although from what I'm hearing, it won't be a problem. He's very confident.
"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."
If Parker does indeed miss out on the Euros it is thought that Liverpool midfielder Jordan Henderson will take his place as he has been placed on stand-by.