Borussia Dortmund tabled a bid worth €26m in guaranteed fees plus €16m in add-ons for the 19-year-old, according to Sky, while Bild reported the offer at €34m guaranteed plus a further €6m in bonuses.
Regardless of the exact figure, Cologne rejected the proposal immediately, with sporting director Thomas Kessler's camp said to have declared negotiations over given how far the offer fell short of the club's £43m (€50m) valuation for the forward.
Koln's hierarchy are also understood to be frustrated with Borussia Dortmund's conduct during the pursuit, unhappy with what they viewed as attempts by the Bundesliga club to influence the player directly in order to make a move more likely. Whether that dispute rules out any deal for El Mala this summer remains to be seen.
Sources close to the player's family suggest they could be open to a move to Dortmund's Strobelallee training base, with Bild going as far as to claim that Signal Iduna Park is the only realistic destination should El Mala leave Koln this summer.
Reports from Express also suggest a deal could be edging closer behind the scenes, despite the public breakdown in talks, with some suggesting the winger could be under contract at Dortmund within a matter of weeks.
For now, Koln remain unwilling to move significantly from their €50m valuation, and relations between the two clubs will need repairing before formal negotiations can resume. El Mala scored eight goals in 25 Bundesliga appearances last season for Koln, emerging as one of the division's most talked-about young attacking talents, and has already been capped at senior level for Germany after being called up by former head coach Julian Nagelsmann.
English side Brighton have also shown recurring interest in the winger over the past year, though Koln have rebuffed their approaches to date, wary of losing further leverage in what is shaping up to be a lengthy transfer saga.