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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Suarez thanked those who supported him via a video message on Tuesday evening, citing his determination to be fit as soon as possible, and Rodriguez is keen to see his team-mate return as soon a possible.
"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 too soon to set a return date for Suarez.
"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."