Not if it’s a reader intended for DESFire chips. I can’t imagine them being dual frequency. DESFire is a “newer” technology that doesn’t interface with the legacy LF systems.
You could request that the system administrator add the UID of the HF side of your NExT to the system. The whole point of a “Unique Identifier” is that only one chip will have it. If it truly does “only scans the UID” then that may work.