The 28-year-old, who is out of contract at the end of the season, could be in line for a Ligue 1 debut against Montpellier on Tuesday.
Fletcher began his career with Edinburgh-based Hibernian and joined Sunderland from Wolverhampton Wanderers in 2012, scoring 23 goals in 108 appearances.
Last season he became the first Scotland player to score an international hat-trick in a 6-1 victory over Gibraltar.
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(Reporting by Martyn Herman; Editing by Tony Jimenez)
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