Sturridge has returned to Liverpool after being ruled out of Friday's World Cup qualifier with Moldova at Wembley.
The 24-year-old has failed to recover from the groin injury he aggravated during Sunday's win over Manchester United.
Sturridge will now have further treatment on Merseyside before it is decided whether he should link up with Hodgson's squad once more before they leave for Kiev.
It is a long shot though. In fact, Hodgson wonders whether the former Chelsea man will be available for the Reds' Barclays Premier League trip to Swansea on September 16.
"We have to be honest here," Hodgson said.
"Sturridge is doing ever so well to try and make himself available.
"He was devastated to turn up injured. He wanted to be with us and to have the treatment so he could play.
"But the fact is when they did the scan at the beginning of the week, it was going to be touch and go for Tuesday, and possibly even Saturday week.
"He wants to be a part of it. He's young and can recover quickly. We hope there's some good news on Sunday morning and he can come with us and take part.
"But I'm not enormously optimistic. I'm not confident. We can't put him out there unless he is fit."