The highly-rated teenager developed his skills during his early years with Altinordu FK before joining Trabzonspor last summer.
Cevikkan arrived at Papara Park for a fee believed to be in the region of £600,000 and while he is yet to make his first-team debut, his performances in age-group football have captured the attention of several high-profile clubs.
The 18-year-old recently represented the Turkey Under-18s, who played out a 1-1 draw against Spain.
While Madrid are expected to strengthen in various positions in the upcoming summer transfer window, including the potential additions of players like Leny Yoro, Kylian Mbappe and Alphonso Davies, they are also believed to be considering bolstering the goalkeeper position.
Real Madrid to move for Cevikkan?
With Courtois facing injury concerns, Andriy Lunin's contract set to expire (although a renewal is likely), and Kepa Arrizabalaga's loan spell nearing its conclusion, Real Madrid are actively seeking promising young goalkeepers to invest in.
As reported by Turkish media and relayed by Fichajes, Los Merengues are now closely monitoring Cevikkan as a potential option in the upcoming summer transfer window.
The report adds that Madrid's scouts have been observing the young goalkeeper during matches with the Turkish Under-18s team and have been impressed by his performances.
Currently the third-choice keeper for the Super Lig outfit, the 1.90 metre-tall teenager is believed to be seen as a possible long-term solution to take up the number one jersey for the reigning La Liga champions.
Carlo Ancelotti's side are no strangers to bringing in players from the Turkish market either, having previously signed Arda Guler from Fenerbahce last summer.
It is also understood that Real Madrid's interest in goalkeepers extends beyond Cevikkan, with Marcin Bulka also being considered for the position.
Los Blancos are currently leading the La Liga standings, eight points above Barcelona with eight games left to play, while they are also still in the running in the Champions League, tied 3-3 with Manchester City after the first leg of the quarter-finals at the Santiago Bernabeu in midweek.