However, Hodgson believes that there is an outside possibility that the 24-year-old could recover in time for the encounter in Kiev.
"He's worked hard at his treatment," Hodgson said in a press conference. "The initial prognosis was that he would not be fit for either of them. We didn't accept that and he didn't accept that either, so he's worked very hard to try and have the necessary treatment.
"I would think it will be touch and go, we won't know until Sunday morning. He reports back on Saturday evening; Sunday morning we have a training session before we leave for the Ukraine and, if he passes it, he'll be with us. If he doesn't he'll be staying with Liverpool."
Sturridge has scored in each of Liverpool's three Premier League matches so far this season.