The Uruguay international sustained the injury in the Champions League semi-final, second leg at Bayern Munich and missed Barca's final two La Liga games, including the 1-0 win at Atletico Madrid when they secured a fifth title in seven years.
"All the available players from the first team trained," Barca said on their website on Wednesday. "Luis Suarez worked with them without yet being given the medical all clear."
Barca are chasing a treble of titles and after hosting Bilbao at the Nou Camp, when they will bid for a record-extending 27th domestic cup crown, they take on Juventus in the Champions League final in Berlin on June 6.
The Catalan giants are the only Spanish club to have won the treble, achieving the feat under Pep Guardiola in 2008-09.
Suarez had a slow start at Barca after his ban for biting an opponent at the World Cup expired at the end of October but has been in impressive form since the turn of the year.
The 28-year-old has scored 24 goals in 41 appearances in all competitions this season and has also laid on 16 assists, developing a fine understanding with fellow South American forwards Lionel Messi and Neymar.
(Reporting by Iain Rogers; Editing by John O'Brien)
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