"He's responding very well and his spirits couldn't be better. He's working full out on his physical fitness," Tabarez said after Uruguay's first practice at their training base near Belo Horizonte.
"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."
Uruguay kick off their World Cup Group D campaign against Costa Rica followed by matches against England and Italy.
Suarez told his Twitter followers on the squad's arrival in Brazil that his left knee is recovering well from his keyhole surgery on May 22 and he is in a good frame of mind.
"I wanted to tell you the knee is going very well, I feel very good, this depends on the day to day (work) but it's on the right track," Suarez said in a 32-second video on his Twitter account.
"I also wanted to thank you all for your support this week and, well, it goes without saying my mind's on the World Cup."
- Sports & Recreation