Website Kick Off is reporting that the Gunners are pondering a move for the former Blues star, whose contract at Atletico Madrid is due to expire at the end of the season.
The same report claims that Luis was linked with a move to French side Paris Saint-Germain in the summer transfer window, but a move failed to materialise as he ended up staying at the Spanish club.
According to the same article, new Arsenal boss Unai Emery is keen to upgrade his options at full-back and is searching for replacements for Sead Kolasinac and Nacho Monreal.
The same story says that Atletico would be likely to accept an offer less than his €30m release clause, as Luis could potentially walk away from the Spanish club for free at the end of this season.
Luis spent one season at Chelsea FC before returning back to Atletico Madrid in the summer of 2015.
Meanwhile, Arsenal have made it back to back wins in the Premier League this season after securing victories over West Ham United and Cardiff City.
The Gunners will look to make it three wins on the trot after the international break when they take on Newcastle away from home later this month.
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