The Uruguay international returned late to pre-season after featuring five times for his national side in this summer's World Cup.
Valverde points to last season, though, when the 31-year-old recovered from a disappointing start to net a credible 25 goals in La Liga, as reason enough to stick by him.
"Luis is fine," he told reporters. "He's only just coming back from his [post-World Cup] break, so he's gradually getting up to speed, but he looks good.
"Luis is a goalscorer. He's aggressive in the area. We know what he gives us. Regardless of his success [in front of goal], the fight is always there.
"Last year, at the beginning, there were criticisms because it took him a while to start scoring, but when he started he did not stop. He guarantees fight in front of the goal. It's a matter of patience and perseverance, and what Luis has is perseverance."
Suarez was a second-half sub in the Joan Gamper Trophy match against Boca, with Malcom, Messi and Rafinha all registering.