United swooped for Obi when he became available from Arsenal over the summer. The 17 year-old has since made three Premier League appearances for United.
Cox recalled to the Manchester Evening News: "Occasionally you get moments like this.
"Arsenal are a wonderful club. They deliver a great program and develop great players. For one reason or another, and it's for Chido and his family to know why, they felt the best opportunities for him may rest away from Arsenal.
"Because he holds a Danish passport, the whole of Europe was open to Chido. We quite simply became aware of the fact that Chido was about to make a move to Europe. He’d been to visit a club and identified the club where he was going to potentially end up. We thought if this player is available and is looking to leave, then we should make every effort we possibly can to sign him."
Cox continued: "In effect, it's a UK-based recruitment search.
"The pretty familiar formula for Manchester United's senior and youth teams has always been having the best local players and adding some of the best talent from further afield," he explained.
"If you look back, it's George Best, it's Bobby Charlton, or it's Duncan Edwards from further afield, added to a group of local lads. Then fast forward and it's someone like Paul Pogba. We have an extensive group of talented scouts who are exceptional at looking at potential in players. We're trying to make sure there's a healthy pool of high-potential talent sitting beneath the first team.
"It was a real concerted effort to sign Chido, so there'd been a lot of work done by our recruitment team led by Luke Fedderenko, and Stephen Ajewole would have played a key role in that as well. Sam Williams too.
"The coaching staff would have played a key role as well because we're trying to present an opportunity. This is our staff, this is our history and track record of developing players. This is what the program looks like, this is the resource that would be available to you. This is how we see the club in the future.
"We had an opportunity to meet with Chido's family and the important people to him. We had a number of conversations that allowed us the opportunity to be the club that he chose to join."
Cox added Obi is delighted with how this first season has developed, though admits senior injuries have played their part.
He said, "He's in a good place at the moment. There have been opportunities to train with the first team and a few opportunities from off the bench.
"But let's be honest, there's been some injuries and some disruption to the squad. The art is to just keep regularly reviewing where a player is at."