They might not have Bluetooth sockets on the logic board to plug them into. I cannot order a bluetooth board for that model on GSX.
From GSX Service Guide:
Check for whether a Bluetooth board is installed or not. iMac 20-inch (Mid 2009) and iMac 21/25-inch (Late 2011) do not come with Bluetooth boards installed.
From EveryMac.com
http://www.everymac.com/systems/apple/imac/specs/imac-core-i3-3.1-21-inch-alumin um-late-2011-education-specs.html
Connectivity includes four USB 2.0 ports, a Firewire "800" port, built-in 802.11a/b/g/n Wi-Fi, Gigabit Ethernet, and an SDXC card slot as well as a single Mini DisplayPort. It doesnot support internal Bluetooth.
Externally, the "Late 2011" iMac uses the same "edge-to-edge" glass design and "seamless all aluminum enclosure" as the "Mid-2011" models. Internally, however, the education-only "Late 2011" iMac is equipped with a slower processor with half the number of cores, less memory, less VRAM, a smaller hard drive as well as no support for Thunderbolt or internal Bluetooth. It also ships with a less capable Apple Mouse.