The defender has only recently returned from a long spell out with an Achilles injury
Laurent Koscielny turned down the chance to join Monaco, opting to stay with Arsenal at least until the end of the season.
The defender only returned to action in the Europa League win over Qarabag in December, having not played since rupturing his Achilles in the same competition in May 2018 against Atletico Madrid.
His injury curse struck again when he was forced to pull out of the FA Cup win against Blackpool last Saturday after picking up a back problem in the warm-up.
According to Le10 Sport, Monaco manager Thierry Henry was interested in bringing his former team-mate to the Stade Louis II this month, but Koscielny declined the offer as he was still working his way back to fitness.
The 33-year-old joined Arsenal in 2010 and is one of their most senior players, having made 330 appearances and winning three FA Cups.
Henry was also turned down by former Real Madrid centre-back Pepe, who returned to Porto after 12 years, so instead signed Naldo from Schalke, with his side 19th in Ligue 1 after just three wins all season.
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