"(Sturridge) felt an injury in training this morning and will go for a scan this afternoon. He will then be assessed by England medics," a statement on the Football Association's website said.
The nature of the injury was not known but should Sturridge be unavailable for the testing trip to Basel, it would be a big blow to manager Roy Hodgson.
The Liverpool player has established himself as the spearhead in England's attack, scoring five times in his 16 appearances for his country.
England face Switzerland, Estonia, Lithuania, Slovenia and San Marino in qualifying Group E. 

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