Real are planning to overhaul their squad in the summer following a disappointing season that’s left the Champions League as their only hope of a major trophy.
And the latest reports from Spain indicate the La Liga giants’ president Florentino Perez is hoping to land Nelson alongside completing a cluster of big money signings.
Nelson’s rise through the ranks at Arsenal has apparently turned the heads of scouts in France as well.
And it seems Real will have a fight on their hands as they look to strike an agreement for the 18-year-old winger.
According to Don Balon, Monaco are looking to sign a replacement for Kylian Mbappe – who joins Paris Saint-Germain permanently in the summer.
And Nelson is said to have emerged as one of their top targets as they seek to bolster their forward line.
Real and Monaco are joined in showing interest in Nelson by PSG.
PSG already boast an attacking line-up that includes Mbappe, Neymar and Edinson Cavani.
But they are supposedly in the hunt for Nelson too as they don’t want to miss out on one of Europe’s top rising talents.
Nelson is under contract at Arsenal until the end of the 2018/19 campaign.
And the Gunners may be forced to sell him this summer with no fresh agreement currently in the offing.
Real, Monaco or PSG could sign Nelson for a minimal compensation fee next year if he does not put pen to paper at Arsenal.