The ex-international attacker has revealed that he was on the verge of signing for Los Blancos, but eventually ended up transferring to Real Betis insteadReal Madrid in the summer of 1996 after Ajax decided to cash in on the winger.
Finidi won three Eredivisie titles during his spell with the Amsterdam giants, as well as one Champions League title and the Intercontinental Cup.
However, the Nigerian fell out of favour after the side lost the 1996 Champions League final against Juventus, and the ex-player has revealed some big teams were linked with bids for him.
"It’s true that a lot of big clubs like Real Madrid and Manchester United showed interest, but it was Real Madrid that almost signed me on," Finidi was quoted as saying by SuperSport.
"My agent even reached a verbal agreement with Madrid, but things broke down at the last moment so I moved to Betis instead."
The 40-year-old also wore the jerseys of Mallorca and Ipswich Town after his spell with Betis, before eventually hanging up his boots in 2004.
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