Murray was scheduled to play in Brisbane before his troublesome right hip injury forced him to pull out and left his participation at the Australian Open in doubt.
As part of his planned practice, Murray sought out Kyrgios to help him prepare for the tournament, but the early wake-up call did not sit well with the Australian.
Speaking to the ATP Tour's official website, he joked: "He [Murray] was actually trying to organise a hit for me at 8am, I said 'Andy, I'm not going to make that hit'.
"I offered him 9am. I thought 9am is pretty good and then he said 8am. I said 'no, you're going to have to find someone else'."
Kyrgios spoke of his disappointment that Murray had to withdraw in Brisbane and is keen to see his friend make a return to the Tour.
"I saw him the next day and he told me he pulled out," Kyrgios added.
"It's pretty sad; he's definitely a fan favourite. He brings a lot of the people to all these tournaments and he's a good friend of mine.
"It's never good seeing a guy like that get injured, especially because he's just good for the sport. He's a good guy as well."
Kyrgios progressed to the last eight in Brisbane with a three-sets win over compatriot Matthew Ebden on Thursday.