According to Goal, Galatasaray approached the Spanish club through intermediaries with a proposal for the 27-year-old.
Despite the attractive financial package and the player’s clear desire to move to the Wanda Metropolitano, Atletico turned down the opportunity.
The club’s hierarchy concluded they do not currently have the financial resources to complete a deal of that magnitude this summer.
Los Rojiblancos are also fully committed to Julián Álvarez as their main centre-forward, alongside Ademola Lookman, and have no intention of selling the Argentina international.
Lookman, who arrived in January, can play out wide or alongside Alvarez in attack, with Alexander Sorloth as the other alternative.
Osimhen currently enjoys a high net salary at Galatasaray, boosted by favourable tax conditions for foreign players in Turkey. His readiness to reduce those earnings underlines how keen he was on a move to Madrid.
However, Atletico’s decision appears final for now, leaving the Super Eagles star’s future still uncertain as the transfer window continues.