The 18-year-old nailed down a regular starting spot at Fenerbahce in the second half of last season, showing signs of living up to the hype that has surrounded him from an even younger age.
Despite coming up short to local rivals Galatasaray in the Super Lig title race, Guler played a central role in a strong finish to the season which sealed silverware for his club.
Guler contributed to 13 goals across all competitions for Fener over the 2022-23 campaign, and played a starring role in Fener's Turkish Cup final success over Istanbul Basaksehir, setting up the opening goal for Michy Batshuayi, before being named man of the match.
Therefore, Marca claims that Real Madrid are becoming serious candidates to land the youngster, who has a release clause of just £16m in his contract.
It would be a deal that would continue Real's recent transfer policy of signing up-and-coming players, with 19-year-old Jude Bellingham already arriving for £113m this summer.
The last few years have also seen Los Blancos bring the likes of Vinicus Junior, Aurelien Tchouameni, Eduardo Camavinga and Endrick to the Bernabeu, a far cry from the years where the club signed ready-made 'Galacticos'.
While not quite having the profile on the level of Bellingham, Guler is also already a full international, having made four appearances for Turkey's senior side.
Born in 2005, Guler scored his first international goal in the recent Euro 2024 qualifier against Wales, claiming the Crescent Stars' second goal in a 2-0 success in Samsun.
This speculation comes exactly 12 years after Guler's namesake and Turkish icon Arda Turan made a move to the Spanish capital from the Super Lig, joining Real's rivals Atletico Madrid for a fee of €12m (£10.25m).
While drawing comparisons to Turan, Guler has also been strongly likened to another star player from another of Real Madrid's big rivals, ex-Barcelona man Lionel Messi, due to his technical style of play and diminutive build.
The Spanish giants are not the only club who are said to be interested in the Turkish international though, as fellow La Liga clubs Barcelona and Sevilla have previously been linked, along with Liverpool, Benfica and AC Milan.