According to Kick Off, Gunners boss Unai Emery is interested in the 33-year-old in order to add further cover to his full back position, having found his side relatively short-changed there so far this season after injury to Sead Kolasinac.
Brazilian international Luis was linked with a move away from Atletico this summer, after Paris Saint-Germain showed significant interest in the player.
However, despite outlining a lucrative contract with Luis, the French side were unwilling to meet the high price demands of Atletico and instead turned to signing Bayern Munich's Juan Bernat.
Spanish publication AS reported that the Parisian giants offered just €5m for the defender, some way off Atletico's €30m demands. Bernat is believed to have cost the club around €14m in transfer fees.
They looked at signing Filipe Luis and even considered Danny Rose for a moment, but it looks like PSG's new left-back will be Juan Bernat from Bayern Munich— Dean Jones (@DeanJonesBR) August 31, 2018
Speaking about his failed move to PSG with Marca, Luis explained: "The opportunity to go to PSG arose and I asked Atletico to free me, in the same way they did with Gabi, but the club understood that it was not the same situation.
"There was little time [until the transfer window closed] and it was difficult to find a replacement. When they said that they did not want [the transfer] to happen and stipulated a price that was not going to be paid, I accepted."
Luis was also keen to distance himself from reports that he insisted on a move away, or that he was unwilling to train with the squad at any stage.
He said: "I have history at Atletico and [the rumours] have left me sad. They tried to make my image worse."
Due to Luis' contract expiring at the end of the season, Arsenal would be able to enter pre-contract terms with the player in January - so that he could join them next season on a free transfer.
However, should Emery want to sign the player sooner, then Atletico are likely going to demand a significant transfer fee once again, especially knowing they're likely to lose the player anyway come the end of the season.