The 35-year-old Benzema has been hampered by niggling injuries at times this season.
According to AS, Los Blancos have set their sights on Haaland, the Norwegian international who currently plays for Manchester City.
Haaland has been in exceptional form this season, scoring 28 goals and providing five assists in 26 Premier League games.
He also equalled Lionel Messi's freak record of scoring five goals in a single UEFA Champions League knockout game, before being taken off by Pep Guardiola in the 7-0 win over RB Leipzig.
So far, Haaland has scored 42 goals in the 37 games he has played for City.
Real came close to signing Gabriel Jesus last summer, but the move fell apart due to the limitation on the number of non-EU players allowed. Now, they are looking to sign Haaland in 2024 after losing out to Manchester City last year.
There were reports doing the rounds that Haaland had a release clause which would become active in 2024. However, it has been claimed that the clause was linked with Pep Guardiola's future at City and since he renewed until 2025, Haaland's exit clause is no longer applicable.
Despite these claims, Real Madrid are not worried and plan to move for Haaland next year. The Premier League top scorer's signing in 2024 will be independent of what happens with the club's interest in Kylian Mbappe. Real are not ruling out the possibility of bringing Haaland, Mbappe, and Vinicius together in 2024.
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The La Liga giants are looking to establish a new order with players like Toni Kroos (33), Eden Hazard (32), Luka Modric (37), and Benzema likely to step away after next season.