Costa is currently nursing the problem, having suffered a setback in his recovery just minutes into his side's Champions League final defeat to Real Madrid last week.
However, La Roja boss Del Bosque has stated that his frontman's likelihood of making it to Brazil next month "looks promising".
"It looks promising," Del Bosque told reporters. "On Friday they will have a scan. If it's good, we will make a decision on Saturday morning."
Costa scored 36 goals last term to help Atleti to their first La Liga win in nearly 20 years.