Kessler stopped short of naming the club at a 'DuMont Talk' event in Cologne-Ehrenfeld, but suggested interest had picked up once word spread that Köln were closing in on the Tottenham winger.
"When there is a public perception that we at 1. FC Köln have a chance to sign a player like that, you can imagine that one or two Bundesliga or international clubs might ask just how certain the deal really is," he said.
Fussball Transfers has speculated the mystery suitor was Borussia Dortmund, who were searching for a replacement for the injured Giannis Konstantelias, sidelined with a torn cruciate ligament, at the end of August.
Dortmund ultimately moved for Ethan Nwaneri on loan from Arsenal instead. Asked directly whether Dortmund had made an approach for Moore, Kessler kept his answer deliberately vague.
"I don't know Borussia Dortmund's squad planning, with the exception of one player, and he's still with us," he said, "but he was clear all along and wanted to come to Köln. Mikey kept his word.
"The talks went well. Now we're happy that he's here."
Moore joined Köln on a season-long loan from Tottenham following a productive spell on loan at Rangers, and said the club's persistence had made the decision straightforward.
"The club showed great interest right from the start. The talks with the management went really well; the prospect of playing in the Bundesliga here and the way the club wants to play made my decision an easy one," he said upon completing the move.
Kessler was similarly effusive in his own welcome, praising the 19-year-old's maturity.
"Despite his young age, Mikey already displays remarkable maturity. He possesses excellent technical ability, is creative and bold in one-on-one situations, and consistently poses a threat in attack thanks to his dynamism and carefree style," Kessler said. "His profile will expand our options in the final third and give us added versatility. We are convinced that he will take the next steps in his development with us."
Moore wasted little time showing glimpses of that potential, making an immediate impact off the bench on his debut in a 4-1 defeat to VfB Stuttgart.