Despite having already signed Trent Alexander-Arnold, Dean Huijsen, and secured a future deal for Argentine wonderkid Franco Mastantuono, Los Blancos are reportedly exploring options to bring in a physically dominant forward who can offer a different style of play.
New head coach Xabi Alonso is believed to be keen on adding a traditional No. 9 to his squad, someone capable of complementing the speed and flair of Kylian Mbappe, who remains the undisputed starter.
According to reports from Spain, Fullkrug is under consideration despite his lackluster debut season in the Premier League, where he managed just three goals and two assists in 20 appearances for the Hammers. Still under contract at West Ham for three more years, the 32-year-old could be available for the right fee due to his struggles to settle in London.

Fullkrug’s prior form at Borussia Dortmund, where he netted 15 times across all competitions and scored in the Champions League, appears to have kept him on the radar of top European clubs.
Real Madrid are not limiting their options to Fullkrug, however. Ante Budimir of Osasuna is another name reportedly under review after a standout 24-goal season in La Liga. Additionally, former Liverpool forward Roberto Firmino—currently at Al-Ahli—is also being monitored.
While speculation continues around the future of Rodrygo, it appears unlikely the Brazilian will be sold due to his high market valuation. Madrid’s focus seems to be on building depth, not reshuffling their core. A deal for Fullkrug would certainly raise eyebrows, but with Alonso’s tactical flexibility in mind, it could offer Madrid a new edge in attacking situations next season.