Real Madrid reportedly watched William Saliba in Sunday's 1-1 draw against Manchester City at the Emirates Stadium.
Los Blancos have been mooted as a potential suitor for a player who has entered the final two years of his Arsenal contract.
The Gunners are keen to agree a new deal with Saliba to secure his long-term future and ward off any transfer interest.
Arsenal are making progress in contract negotiations, but there is no immediate sign that Real Madrid are willing to end their interest in the France international.
Real Madrid watch Saliba in Man City draw
According to TBR Football, Real Madrid personnel were in attendance at the Emirates Stadium for Arsenal's 1-1 draw with Man City on Sunday.
Los Blancos were allegedly there to keep a close eye on Saliba's performance in the centre of the Arsenal backline.
The Frenchman played the full duration of the contest, which saw Gabriel Martinelli net a stoppage-time equaliser to salvage a point for the hosts.
Saliba has started all four Premier League games for which he has been available this term, demonstrating his importance to Mikel Arteta's side.
As a result, Arsenal will be desperate to retain Saliba's services despite having alternative centre-back options in Gabriel Magalhaes, Piero Hincapie, Cristhian Mosquera and Riccardo Calafiori.
Why are Real Madrid targeting Saliba?
Real Madrid appear to be on the lookout for a new long-term central defensive partner for summer signing Dean Huijsen.
David Alaba is expected to leave Los Blancos at the end of the season, while it remains to be seen whether Antonio Rudiger will extend his stay, having entered the final year of his contract.
Xabi Alonso's side have been linked with potential targets who become free agents at the end of the season, including Crystal Palace's Marc Guehi and Liverpool's Ibrahima Konate.
However, they are keen to sign the best player possible rather than just basing their decision on the financial benefits of recruiting a free agent.