Suarez suffered meniscus damage in his left knee and has since undergone surgery to remedy the issue, leaving his ability to feature at the World Cup, which starts on June 12, in question.
However, Uruguay have refused to rule the former Ajax man out of the tournament directly after the operation, and team doctor Alberto Pan insisted they have seen nothing to change that opinion since.
"The core of the concept of his return was expressed in the initial statement made in the immediate post-operative period and we can happily say that Luis' participation in the World Cup is not ruled out," Pan said at a press conference in Montevideo.
"It is very risky to give exact dates. We cannot have absolute certainty or clear numbers but the postoperative period has been very good.
"Luis is not ruled out of the World (Cup), but you cannot talk about specific times. Luis is very positive, I never heard a negative expression, and he says it is better every day.
"Today (Suarez) is painless (and) is working on fitness and supporting essentials."
Suarez is likely to be key to Uruguay's hopes of enjoying a strong World Cup having topped the scoring charts in the CONMEBOL group in qualification for the tournament with 11 goals.
"What happens with Luis will depend on the evolution of his knee," Tabarez said.
"We have no doubt about his enthusiasm and condition but our main concern is the health of the player."
