The Liverpool striker felt some discomfort in his knee during a training session on Wednesday and is reportedly set to undergo surgery later this week.
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He said: "According to the report I received a while ago, we are optimistic that he can go to the World Cup.
"He has a sore knee and was subjected to tests. It happened so fast, just a few hours ago. The intention was to keep everything quiet and report today through AUF accounts on social media. We found out at night because it all happened late that night.
"Suarez trained with a bit of pain and decided to have an MRI. Until a while ago, the last information I had was that they were deciding what to do. I cannot say anything else."
England and Italy make up Group D, with Roy Hodgson's men set to face Uruguay on June 19.