Diaz, 28, secured a €75 million move from the English champions to their German counterparts earlier in the summer.
The Colombia international has taken to the club like a duck to water, scoring three goals and providing two assists in his four games across all competitions.
Speaking to ESPN, Gakpo, 26, revealed Bayern open talks with his representatives before ultimately deciding to sign Diaz.
He said: "From what I understand, they (Bayern) did come (to open talks about a transfer), but they ended up buying Luis Diaz. It's difficult because so much is happening.
“Other clubs are approaching you, but you might want to stay with your own club. Everyone handles that in their own way, but it's definitely difficult. When the future is uncertain, it just becomes a very difficult story."