Quaresma is doubtful with a muscle problem in his right leg and trained separately from the rest of the squad at the Stade Geoffrey Guichard on Monday.
Asked about the player's availability, Santos told a news conference: "There are still 24 hours to go and even 12 hours can make a difference. I will decide tomorrow whether he will play or not."
Quaresma, 32, scored twice and set up two more goals in the 7-0 demolition of Estonia last week, Portugal's final warm-up game.
Fenerbahce's Nani is standing by to replace him alongside talisman Cristiano Ronaldo in attack.
Nani started just one of Portugal's three warm-up games, a 1-0 defeat by England on June 2, and was replaced by Quaresma after 61 minutes.
Ronaldo, who scored 51 goals in 48 games in all competitions for Real Madrid this term, was also bothered by muscular problems at the end of the season.
"He is very well. He is really motivated," Santos said of Ronaldo.
Portugal reached the semi-finals four years ago before being eliminated by Spain on penalties.
After their opener, Portugal take on Austria on June 18 in Paris and Hungary four days later in Lyon.
(Writing by Cindy Garcia; Editing by Tony Jimenez)
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