The 29-year-old, who joined Arsenal in 2011, has made 36 appearances for the Gunners although he has struggled to adjust to the demands of English football.
Manager Arsene Wenger signed Spaniard Nacho Monreal on the final day of the January transfer window, unwilling to promote Santos to first-choice left-back in the absence of the injured Kieran Gibbs.
Brazil international Santos joined Arsenal from Turkish club Fenerbahce who he played for after spells in Brazil with Corinthians, Atletico Mineiro, Flamengo and Figueirense.
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