The Nexus Player only comes stock with 4GB of storage. This is practically nothing in this day and age. In fact I can remember the first PC my family ever bought included a 3GB hard drive! Which of course back then was plenty, but now there are some apps that can take up all of that space. The good news is that "DeesTroy", known for his TWRP development, has figured out a way to add storage to the device using a standard OTG cable. He was able to attach a 64GB SSD with USB OTG and a repackaged boot image to use the SSD for the userdata partition only. If you are planning to use an SSD you can find the boot image Dees Troy used at the link below. otherwise you might want to see if a usb thumb drive will work with your OTG cable. Report back here with your findings!
via +DeesTroy