Agger suffered concussion after a knock in the second half of the 1-1 draw at Anfield. He will not be in the squad to face Trabzonspor in the Europa League on Thursday and could be a doubt to face Manchester City in the Premier League on Monday.
Hodgson said: "Daniel is not doing that well. It is three days after the incident and he is still suffering from the concussion. He has no memory of the game. It was quite a serious concussion he received and we can only hope it will settle down in time for Monday's match against Manchester City. There was never any question he would be fit for tomorrow. He is not able to do very much at the moment because he is still suffering from headaches.
"Even something as simple as reading a newspaper or watching TV can give him a headache so it is just a question of him taking things easy.''
Midfielder Javier Mascherano will also miss the clash against the Turks with a calf injury but could be back in contention for Monday's trip to Eastlands.
"He will always be in my plans until the day comes when he leaves the club,'' Hodgson said. "For me that will be a long time in the future. If I could get my wish, he would always play.''
Hodgson is hoping that Holland winger Ryan Babel, who has been linked with a £9 million switch to Wolfsburg, will stay.
"I'm afraid we are in the realms of speculation,'' Hodgson said. "You know how many stories you are getting every day, and many of them are completely unfounded, many of them are just really attempts to put their players in the spotlight. We've had no written or formal offers for Ryan Babel and he is a player I am expecting to play for us.''