The Brazilian player showcased his talent last season while on loan with Serie A club Frosinone, despite the team's unfortunate relegation.
The Athletic says Championship club Norwich are now in talks with Real about a new loan for Reinier.
The Canaries see Reinier as a replacement for Jonathan Rowe, who has just been sold to Olympique Marseille.
Talks are now underway between Real and Norwich with the aim of a loan-to-buy arrangement.