Suarez underwent knee surgery on May 22, and is back in training with Tabarez's squad as he races the clock to be fit for Uruguay's Group D opener against Costa Rica on June 14.
But Tabarez said it was so far, so good for the Liverpool striker.
"So far things are going very well, so the plan that was set by the medical team continues," Tabarez said.
"That makes us hopeful that his improvement continues but we don't want to set any deadline or prediction."
Tabarez said Suarez had not yet begun any running on the training pitch, which puts a cloud over him participating in the early stages of the tournament.
"To the extent that he exceeds certain demands he will move on to more demanding training," he said.
"The last thing he did was cycling and aerobic work, he has worked with the elliptical (cross-trainer), which is a step more.
"Depending on how he responds we will see if he will be in condition to take the pitch to walk or run."
Tabarez said his squad had prepared well ahead of their opening match in Fortaleza.
"There are still three training sessions before leaving on Monday and I think... we will arrive in Brazil in good condition," he said.
