The Tottenham left-back sustained an injury as his side beat Cardiff 1-0 at the weekend, and was taken off in the closing minutes.
Rose had a scan on Monday and is being monitored by the FA's medical staff, but is reportedly keen to remain with the squad even if he has no chance of playing.
He joined Danny Welbeck and Alex McCarthy on the sidelines at England training on Tuesday morning
All three had individual recovery and conditioning work away from the main group.
The rest of the squad trained as normal although Jadon Sancho, Harry Kane, Jordan Henderson, John Stones and Kyle Walker were all given lighter workouts than the rest of the squad.
England will take on Croatia on Friday in the UEFA Nations League.