The Atletico Madrid man has been struggling with a hamstring injury in recent weeks and was forced off early in their final La Liga outing as well as the UEFA Champions League final.
With the 25-year-old a potential doubt for the World Cup in Brazil, it was confirmed on Sunday that the Royal Spanish Football Federation will now be responsible for his medical treatment in the run-up to the competition.
And Del Bosque, who delayed naming his final 23-man squad, says the forward will have every opportunity to recover from the complaint.
"Diego has got a muscular injury, we're monitoring him closely and keeping an eye on how it evolves," he told Cadena SER.
"We will wait until the last minute before making our decision.
"We're not doing this on a whim - we have until June 2 to submit the list of 23 players and so we have no reason to be hasty.
"I really hope he makes it, but if he doesn't we have other options."
Atletico team-mate Juanfran and Manchester City winger Jesus Navas also have injury doubts for Del Bosque as Spain prepare to begin their defence against the Netherlands on June 13.
