Sturridge has been out of action since sustaining a thigh injury during the previous international break at the start of September.
The 25-year-old was once again missing for Liverpool's 1-0 defeat to Basel in the UEFA Champions League on Wednesday, but Rodgers is hopeful that the former Chelsea striker could be fit to at least be named on the bench for Saturday's Premier League clash with West Brom.
However, the Northern Irishman stated that Sturridge should not be included in England's squad for their upcoming double-header with San Marino and Estonia.
It appears that there will be no conflict of interest, however, as England manager Hodgson will apparently not include Sturridge when he names his party later on Thursday.
"I spoke to Roy. I am not sure if Daniel will be fit for the weekend so I think at this moment he won't be in the squad," Rodgers told reporters after the Basel game.
"I think over the next couple of weeks Daniel has to get up to speed and hopefully after the international break he will be able to play for us, which is the priority."
Sturridge, who scored 24 goals in all competitions for Liverpool last term, but has been restricted to just three Premier League outings this campaign, scoring once.
