Reschke previously worked for the Bavarian
He had identified Davies as a potential signing for his new employers, too, but Bayern had the financial muscle to beat them to a deal.
The 17-year-old joined Bayern from Vancouver Whitecaps in a deal worth $13.5 million (€11.5m/£10m), an MLS record, and Reschke has confirmed that his side
"Congratulations, FC Bayern," he said to AZ.
"We were in Vancouver at the same time as Bayern and tried to sign this guy. But Bayern had a few more important points on their end to sign him."
Davies has enjoyed a fruitful spell at Vancouver, scoring five times and providing 10 assists, leading to reported interest from Liverpool and Hoffenheim, as well as Stuttgart and Bayern.
Stuttgart have one of their own in demand, with Benjamin Pavard attracting interest from across Europe after a stunning World Cup.
Reschke, though, believes he will remain at the club until the summer, at least, despite having the ability to play for an elite club.
"With Benjamin Pavard there was this one moment in which we realised that he is ready to stay with us for one more season," he added.
"Benji has the level to play for every top European club and we fully respect if he does from July 1st 2019 on.
"He has very good offers which we know about because we have a very open relationship. He is outstanding in duels, has a great heading game and strong initial play. The club which will sign him