The Reds have been in discussions with the England camp after their striker picked up an injury during Wednesday’s international friendly against the Republic of Ireland
Sturridge was stretchered off the field shortly after crossing for Frank Lampard’s equaliser during the 1-1 draw with suspected ankle ligament damage.
The 23-year-old has undergone a scan on his ankle, and will definitely miss England’s trip to Rio to take on Brazil at the Maracana Stadium on Sunday.
"He's not going to Brazil," England manager Roy Hodgson told reporters after the match. "He had a good start and we were sad to lose him.
"He hadn't played for a while and was carrying a slight injury. I fear it will keep him out for a few weeks."
Sturridge was making his first start for England after a blistering end to the season at Liverpool, scoring 10 goals in 14 Premier League appearances.