Portugal, coached by Fernando Santos, will hold a training session at St Etienne's Stade Geoffrey-Guichard later on Monday, the same venue where they will face Iceland.
Quaresma scored twice and set up two more goals in his national team's 7-0 demolition of Estonia last week, Portugal's final warm-up game for the tournament in France.
Should Quaresma fail to pass the fitness test, Fenerbahce winger Nani is expected to take his place in the starting side, alongside former Manchester United team mate Cristiano Ronaldo in the attack.
Nani started just one of Portugal's three warm-up games, a 1-0 defeat to England on June 2 and was replaced by Quaresma after 61 minutes.
(Reporting Adriana Garcia; Editing by John O'Brien)
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