Colombian winger Diaz joined Bayern Munich from Liverpool in a £66M deal earlier this summer, and has made a strong impression on Kompany with his fitness and focus.
"He's the most advanced of all physically and mentally," Kompany said. "He had a very good preseason with Liverpool and was already training three weeks ahead of us."
Kompany also discussed Bayern's current squad depth and injury situation ahead of their first Bundesliga clash against RB Leipzig.
"We have so much talent, but the most important thing is that the boys are fit," Kompany said. "At the moment, we're missing Jamal Musiala, Alphonso Davies, Hiroki Ito, and Aleksandar Pavlovic. We can make progress when the boys come back."
Kompany was also asked about his transfer wishes, and emphasized the importance of his existing squad.
"In a healthy club, people communicate daily, and that's certainly the case with us," Kompany said. "We're always communicating, not just about the squad. But everyone has their role. For me, the only important thing is that this squad performs as best as possible."
The Bavarians face Grasshoppers Zurich in a friendly on Tuesday before meeting Stuttgart in the DFL-Supercup final next Saturday.
Diaz will be crucial to Bayern's success next season, but it's clear that the team needs more signings to build a strong squad.