Alonso damaged the ankle in Friday's 2-1 win over Chile and had to be replaced midway through the second half by Javi Martinez but Del Bosque said he had completed a training session at Cape Town's Green Point Stadium on Monday.
"He trained well," Del Bosque told a news conference. "Maybe tomorrow his ankle will be swollen, we'll have to wait and see," he added. "But I think he is in good enough shape to play."
Spain and Portugal, ranked second and third in the world respectively behind Brazil, have never met at a World Cup tournament and the winner of Tuesday's clash will play either Paraguay or Japan in the quarter-finals.
Beyond that, Argentina or Germany await in the last four.
Del Bosque batted away the inevitable question about Portugal's former World Player of the Year Cristiano Ronaldo, saying the European champions were not obsessed with how to thwart him.
"The most important thing is to focus our attention on the Portuguese team as a whole," he said.
"They have proved in both defence and attack that they are a very complete side.
"Thanks to the hard work of their coach (Carlos Queiroz) they have arrived at this World Cup in top condition."
Spain left back Joan Capdevila, who will have Ronaldo bearing down on him on Tuesday, said the best way to stop the forward was by working as a team.
"When you are up against someone like that, one of the best in the world with the speed that he has, it's tough," he told an earlier news conference.
"He'll be roving around the whole offensive area and our four defenders will have to be on their guard.
"We'll have to watch out for him and the other players following behind who are also dangerous."
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