The striker was forced into an early exit during the Champions League final after tearing his hamstring, and could be forced out of La Roja's 23-man World Cup squad
The Atletico Madrid forward tore his hamstring in his side's Champions League final defeat to Real Madrid, which has resulted in del Bosque delaying finalising his 23-man squad - and he may even wait until the Fifa deadline on June 2.
But, despite being optimistic earlier in the week, del Bosque has questioned whether the 25-year-old will be fit for the reigning world and European champions.
"I'm not sure Costa will make it," Del Bosque told reporters.
The 63-year-old added that there was still time for the Brazil-born star to recover, but that he wants him to be fully fit if he is to make the final cut.
"We've still got time but now it's in the hands of the doctors and the medical team. We have to be cautious," he said.
Costa was the subject of much controversy when he opted to play for Spain rather than Brazil, back in March.
He made two friendly appearances for the Selecao in 2013 before making his international debut for Del Bosque's men against Italy.
Even if the star misses out, Spain have plenty of attacking talent, with Fernando Torres, David Villa, Fernando Llorente and Alvaro Negredo among their other striking options.