Borussia Dortmund's proposal, worth around €34m plus a further €10m in bonuses, fell well short of what Koln's board are demanding for the 19-year-old, who has become one of the Bundesliga's most in-demand young talents.
Asked directly about the situation by the Ruhr Nachrichten, sporting director Lars Ricken declined to be drawn on Dortmund's next move.
"He's a player for 1. FC Koln. I understand your question, but you know we don't give status updates on any rumours," Ricken said, before adding more generally that there are "of course many players who would fit in well with us.
"We now have a very good mix in the squad - experienced players, professionals with a lot of resilience, and talents who can develop and take on responsibility.
"Coming into a squad like that is definitely easier for new signings. Niko Kovac has managed that very well."
Cologne have been keen to stress in recent days how enthusiastically El Mala continues to train, insisting there is no question of any defiance or unrest on his part.
Even so, his desire to leave is understood to be firmly established, and with four weeks still to run in the transfer window, it would be something of a surprise if the two clubs failed to find common ground before it closes.
Koln's confidence in holding out for their valuation is rooted in the strength of El Mala's contract, which runs until 2030, meaning the club face no pressure to sell at a discount even with a rival as determined as Dortmund pushing hard.
The saga carries a certain irony given reports that Dortmund could have signed El Mala for a fraction of the current asking price back in 2024, when a disagreement over a fee as small as €200,000 saw Koln step in and secure him instead.
Interest in the winger has not been limited to the Bundesliga's traditional heavyweights either, with reports in recent weeks linking him to clubs including Bayern Munich, Barcelona and several sides from the Premier League, underlining just how highly his rapid development this season has been rated across European football.