"Said El Mala is not a Borussia Dortmund player and he will not become one this summer either," Ricken told the Funke media group.
"We've had open discussions with the people at 1. FC Köln over the past few days, but they rejected our latest offer.
"Borussia Dortmund will not submit another bid and will not pursue a transfer for the player any further."
Dortmund's final proposal was worth in the region of €48m plus around €7m in bonuses, taking the total package close to €55m, according to German reports, but Cologne held firm on their demand for a guaranteed fixed fee of €50m rather than a structure reliant on add-ons.
The gap between the two clubs' positions proved impossible to close despite what both sides described as constructive talks.
El Mala, 19, broke through emphatically last season, scoring 13 goals and adding four assists in 34 Bundesliga appearances, 20 of them starts, form that had made him one of the most sought-after young players in German football and earned him recognition at youth international level with Germany.
Dortmund's interest was long-standing — the club had explored signing him as a teenager from Viktoria Köln in 2023, with a medical reportedly scheduled before he opted to join Köln's first team instead, a piece of history that added extra intrigue to this summer's pursuit.
Internally, Dortmund had reportedly set a new threshold for approving high-value transfers this summer, requiring sign-off from head coach Niko Kovač, Ricken and sporting director Ole Book together before any major deal could proceed.
All three were said to be in favour of signing El Mala, whose fee would have comfortably surpassed the club's previous transfer record — the €35m paid to Stade Rennes for Ousmane Dembélé.
El Mala remains under contract at Köln until the summer of 2030, giving the club no pressure to sell before the deadline, and they continue to face competition of their own for places up front, with Ragnar Ache and a possible arrival from Bologna, Thijs Dallinga, among the options in their squad. Dortmund are now expected to explore alternative attacking options, with Greek playmaker Giannis Konstantelias of PAOK Salonika among the names mentioned as the club looks to add width to its forward line before the window closes.