The surgery put Suarez in doubt for next month's Copa America – with Uruguay set to open their campaign against Ecuador on June 16 – however Tabarez has "high hopes".
Nuevo entrenamiento de la Celeste preparando la @CopaAmerica.— Selección Uruguaya (@Uruguay) May 25, 2019
Gastón Pereiro, Maxi Gómez, Federico Valverde, Martín Silva, Jonathan Rodríguez, José María Giménez y Diego Godín volvieron a trabajar en el Complejo Celeste. pic.twitter.com/0bHEa5d9dy
"I think yes, I hope so, he's working well," Tabarez told reporters when asked if Suarez will be fit for the tournament. "I can't give you details but he keeps us updated through videos and images.
"He's working on his recovery and I know the meaning Luis gives to these things, I know he'll give 100 per cent to be fit when the competition starts.
"I don't want to rush, injuries are always due to circumstances, not to the players' will, he's got his mind set on the recovery.
"He's very professional about it and he has a good record on it, so I have high hopes to have him ready on our team, he's very important to us."
Uruguay – who reached the 2018 World Cup quarter-finals – failed to progress beyond the group stage of the Copa America three years ago.
For the 2019 edition, Uruguay will face Ecuador, defending champions Chile and guests Japan in Group C.