The Gunners are seeking reinforcements for Mikel Arteta's squad.
Arda Guler has struggled for starts at Real Madrid
And they see similarities with their club captain Martin Odegaard.
The Norwegian, 25, had arrived at the Bernabeu as a highly-rated teen, but found game time hard to come by during the first half of the 2020-21 season.
In January 2021 the Gunners moved to sign him on loan, before making the deal permanent in the summer.
Odegaard has gone on to be a huge success at the Emirates and is now viewed as one of Arteta's most important players.
According to Spanish outlet Sport, Gunners chiefs believe that something similar could happen with Guler.
The Turkish wonderkid, 19, arrived in Madrid from Fenerbahce in the summer of 2023.
Amid several injuries and stiff competition, he has struggled for minutes under Carlo Ancelotti.
They claim that he has become unhappy with the situation, having made just three LaLiga starts so far this term.
Martin Odegaard struggled for game time at Real Madrid
Gunners chiefs are claimed to have "made contact" with Guler's entourage as they plot a potential move.
But they are set to face fierce competition, with other teams having reportedly done the same.
Guler has made 24 appearances in total for Real Madrid, scoring six goals.
Last season he was scuppered by knee and muscle injuries, being limited to just 10 LaLiga outings.
The teenager has already become a key man for his country.
He starred at Euro 2024, scoring against Georgia and laying on assists vs Austria and the Netherlands.