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The 18-year-old attacking midfielder has verbally agreed a deal with the 2019-20 Bundesliga runners-up and is set to move on a season-long loan with an option for another year.
Leverkusen had initially been the favourites to sign the Brazilian teenager, who plays in the same advanced midfield role as Havertz, which indicated they were set to allow the Germany international to leave Bay Arena.
Havertz has been heavily linked with a move to Chelsea, with manager Frank Lampard revamping his attacking options having already signed Timo Werner and Hakim Ziyech this summer.
However, with negotiations dragging over a reported €100 million fee (£90m/$118m) for Havertz, representatives of former Flamengo youngster Reinier began to explore other options for him, and now Dortmund have emerged as the most likely destination as he seeks first-team opportunities.
Real are keen to send Reinier to a major European club and view the Bundesliga as the perfect location for his technical skills to flourish. Dortmund can offer him Champions League football next season, a step above Leverkusen who qualified for the Europa League.
The teenager - who is also wanted by La Liga side Real Valladolid, majority owned by Brazil legend Ronaldo- has a contract at Santiago Bernabeu until 2026 and he is regarded as a serious prospect for the future.
Reinier - who finished fourth place in Goal's NxGn 2020 list of the best young talents in world football- has only made three appearances for Castilla, Real's reserve team, since moving to Madrid in January for €30m (£27m/$35m)with a muscle injury and the coronavirus crisis stunting his opportunities in Spain thus far.
However, in the one Castilla game where he completed 90 minutes - against Coruxo in the Spanish league's third tier - he scored twice, and he is viewedas being in the same burgeoning bracket as Real's other young Brazilian attacking talents Rodrygo and Vinicius Junior.
With Flamengo, Reinier helped themwin the domestic title inBrazilin 2019, while he was also part of their successful Copa Libertadores-winning squad.