The 18-year-old is said to be the latest jewel to emerge from Brazilian football and is widely tipped to have a big future ahead of him at the top level and joined Madrid from Flamengo in January.
A report in Diario AS now claims Dortmund are serious in their attempts to secure his signature in a similar arrangement they had for Achraf Hakimi over the past two seasons.
Reinier needs two uninterrupted years in Spain to obtain nationality and that is why Madrid’s preference for him has been to join another La Liga club.
However, they believe he can play in a more important team in Germany and would be guaranteed regular minutes for his development.
The player was originally incorporated into Madrid’s Castilla team but the club now want him to play at a higher level.
Madrid beat off competition from Barcelona and Manchester City to land the teenager in January, as they paid South American champions Flamengo a reported €30m to secure his signature.
Reinier only debuted for Flamengo – who won the Copa Libertadores in 2019 along with the Brazilian top-flight – last year but scored six goals in just eight starts in the league.
Reinier has a long-term contract in the Spanish capital until the summer of 2027.