Suarez has been sidelined since he sustained a hamstring injury during the second leg of Barcelona's Champions League semi-final win over Bayern Munich.
"He's fine," Enrique told reporters on Friday. "He trained all week and, in principle, he's available, as is any other player in the squad."
Enrique was also quick to dismiss rumours that Barcelona already have their sights set on beating Juventus in the Champions League final on June 6 in Berlin as they are expected to have no problems defeating Bilbao.
"We haven't made that error once this season, so why would we do it now before the Copa final?," Enrique said. "We're playing in our own stadium, there are so many things stimulating us and making us stronger. The motivation and hope is extraordinary at the moment.
"The situation is the best of the season, we've had great games, we've got great results and now there's two to go – the two final steps and the culmination of an exceptional season.
"We've seen situations over the years where teams play cup finals at home and it's gone the other way, so we won't know [whether it is an advantage] until tomorrow [Saturday].
"It's a familiar venue but with a different atmosphere. There will probably be more Bilbao supporters than our own but to whom does it benefit? I'll tell you after the game."
The 45-year-old also made it clear that Barcelona will not underestimate Bilbao as he doesn't want his side ruining their chances of winning their second treble in six years.
"Bilbao are one of the teams that most people want to avoid," he said. "They are one of the most uncomfortable teams to play against because they continuously press the ball. Athletic also know us perfectly, so it will be an attractive match."