Sturridge returned to Merseyside after being ruled out of Friday night's World Cup qualifier with Moldova at Wembley and is also a doubt for the Three Lions' clash against Ukraine on September 10.
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 from Liverpool's medical staff 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 when Liverpool put their 100 per cent start to the season on the line at the Liberty Stadium.
"We have to be honest here," said Hodgson.
"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.
- Sports & Recreation