The Manchester City player did not travel with the squad to the North East for Friday's friendly against Australia and has been placed on the standby list.
"Delph is not with us," Hodgson said at Thursday's news conference.
"He's stayed in Manchester. That means he probably won't be in the 23."
Hodgson will cut his current 26-man squad by three over the weekend, before Uefa's deadline of 31 May for squads to be submitted.
Delph's season had been affected by injuries, with the former Aston Villa player making only 30 appearances for City.
Liverpool forward Daniel Sturridge has also missed training for two days because of a calf problem and did not play in Sunday's 2-1 win over Turkey.
Hodgson said that uncapped 18-year-old striker Marcus Rashford would play a "serious part in the game" against Australia and that Manchester United club-mate Wayne Rooney would be on the bench.
"I'm more than content that Rashford will handle that situation," Hodgson said.
"It is a big game for him because I, my coaching staff, the rest of the players, he himself, the whole of the English football world will be looking to say 'we all think this lad's got something special... can he show it to us once again?'.
"We'll be giving him every chance to do so and he'll get so much help, so much support and so much encouragement from the rest of the team."
Southampton's Fraser Forster will replace Manchester City's Joe Hart in goal against the Socceroos.
Friday's match against Australia at Sunderland's Stadium of Light is the second of three warm-up games before Euro 2016, which starts on 10 June in France.