Alonso was left in considerable pain after a heavy challenge against Chile
Xabi Alonso returned to training on Monday, boosting his chances of playing in Spain's last-16 match against Portugal in Cape Town on Tuesday.
The midfielder suffered an ankle sprain in Friday's 2-1 win over Chile and was forced off in the 73rd minute.
However, Alonso appeared to struggle during certain drills, keeping weight off his troubled ankle.
Striker Fernando Torres is also a doubt because of a muscle problem, while defender Albiol is ruled out.
The Real Madrid centre-back, who had not been used in any of Spain's group games, fell awkwardly in Saturday's training session and injured his right ankle.
Spanish team doctor Oscar Luis Celada remained optimistic for Alonso's chances after assessing the results of an X-ray on the ankle on Saturday.
He said: "The first X-ray confirmed that Alonso had sprained his right ankle when he was violently tackled.
"But we are optimistic that he will be fit for the second-round match."
Highlights - Chile 1-2 Spain
Spain's victory, which secured top place in their group, has come at a cost.
Liverpool star Torres, who has yet to score in the tournament, was substituted after 60 minutes against Chile.
However, Spain coach Vicente Del Bosque said after the match that Torres was taken off purely as a precaution, and not a recurrence of a knee injury.
"He felt a spot of muscular bother, nothing to do with his knee injury," stated Del Bosque.
If Spain beat the Portuguese in Cape Town, they would then face a quarter-final against either Paraguay or Japan.
Del Bosque's side, one of the pre-tournament favourites, could meet either Argentina, Mexico, England or Germany in the last four.