Yamal, 18, has been managing groin issues and a hamstring injury suffered in April, while Williams and Munoz have also been recovering from injuries.
The trio remained at Spain's training base in Chattanooga, Tennessee, to continue their rehabilitation rather than travel with the squad for Monday's final warm-up match against Peru.
"If there are no setbacks in the coming days, we expect them to be available on the 15th," De la Fuente told reporters.
"I think all three will be in a position to play."
Asked whether the players could be ready to start against Cape Verde, De la Fuente was more cautious.
"All three are within the expected timelines to arrive in good condition for June 15," he said.
"The most important thing is that those timelines are being met and will continue to be met, so they can be with us and available to be selected at some point in the match."
Spain face Peru in Puebla before travelling to Atlanta for their World Cup opener and De la Fuente said they would not take their opponents lightly.
"For us, this is a very important match," the Spaniard said. "We are not approaching it simply as a preparation game."
Spain arrive at the World Cup among the leading contenders after their Euro 2024 triumph, with a Goldman Sachs model giving them a tournament-high 26% chance of lifting the trophy.
Forward Yeremy Pino said Spain were embracing expectations.
"The favourites tag is normal," Pino said. "We've had some very good years and we carry that with a lot of pride.
"Pressure should not make us play worse. It should make us improve and play better."