The Liverpool striker underwent surgery on a knee injury less than three weeks ago, and is now expected to be fit for his side's second group game - against England on June 19.
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"He is very focused. He is working in double and triple shifts and we hope to have him with us soon," Rodriguez told reporters.
Uruguay head coach Oscar Tabarez echoed his midfielder's sentiments, but admitted it is still too soon to set a return date.
"He's responding very well and his spirits couldn't be better," Tabarez said. "He's working full out on his physical fitness.
"As we have no set deadlines, I don't know if we'll have him for the first match, for the second, for the third. If it were up to me, Suarez would play tomorrow."