The 19-year-old was linked with a move to Manchester United before his £18.5million switch to Dortmund from Red bull Salzburg in January.
Real Madrid are desperate to fill the void left by Cristiano Ronaldo following his move to Juventus in 2018.
The La Liga giants haven’t won La Liga since 2016-17, finishing third behind Barcelona and Atletico Madrid in the last two seasons.
Last summer’s big signing Luka Jovic has scored just twice in 24 games, and will likely be moved on, and Karim Benxema’s time at the Bernabeu is coming to an end.
Rodrygo and Vinicius Jr are talented but raw, with a proven goalscorer seen as a priority by Zinedine Zidane.
And Marca claim Haaland is destined to join Madrid this summer in a deal which could cost up to £100m.
The Norwegian star has scored an incredible 36 goals in just 31 matches for Salzburg and Dortmund this season.