According to transfer reporter Fabrizio Romano, personal terms are already agreed and the 21-year-old is scheduled to undergo a medical and sign for the German club next week. Koln are expected to pay Sydney FC a fee in the region of €1million (£860,000) for a player the A-League club signed on a three-year deal only last July.
Okon-Engstler is not new to life in Europe, having previously been on the books at Benfica's academy in Portugal before returning to sign for Sydney FC.
Speaking after Australia's exit from the World Cup, Okon-Engstler reflected on an emotional end to the tournament and the motivation it has given him going forward.
"Obviously very emotional, very sad, that we weren't able to progress to the next round of the World Cup," he said.
"Just seeing some of the older players and how emotional they were, knowing that it's their last World Cup ... it really hit me, I think, after the game.
"It just makes me even more grateful to experience it ... it gives me so much motivation to go back to keep improving every day and try and play at the highest level every week."
Okon-Engstler was born in Belgium while his father, former Australian international and current Socceroos assistant coach Paul, was playing in the Belgian Pro League. He moved to Australia in 2006 as a one-year-old when his father signed for the Newcastle Jets.
Should the move to Cologne go through as expected, Okon-Engstler will follow in the footsteps of former Socceroo Josh Kennedy in making the switch to German football, and will link up with head coach Rene Wagner, who was handed the job on a permanent basis in May after steering the Bundesliga side away from relegation as interim boss.
He is one of several members of Australia's young World Cup contingent attracting attention from Europe, with 18-year-old defender Lucas Herrington also weighing offers from clubs including Barcelona, Liverpool and Bayern Munich after a standout tournament in the United States.