You'll need a MCU with USB host support, which is becoming rather common these days. Look for USB "OTG". (Also define if you need USB HS or just FS, that will narrow your options of MCUs.)
With such a MCU, as long as it has an embedded USB PHY (again a lot of choice these days, a bit less for USB HS though), you won't need any extra IC.
The "hard" part will be to implement the USB audio class as host. While most MCUs having USB OTG come with a few examples for USB host, those examples usually deal with the simple HID (keyboard, mouse, ...) classes, or the mass storage class. I've never seen vendor-provided libraries/examples implementing the audio class for USB host. That may exist, but specifically look for this.
You could alternatively use TinyUSB if the MCU is supported, but I'm not sure TinyUSB supports the audio class for USB host. That'd need to be checked.
To sum it up, finding a MCU with USB OTG, either FS or HS depending on your needs, will be easy. The hard part is probably going to be the firmware side.