It would appear from your description that the CD player is emitting RFI (radio frequency interference) in the same band the FM stations are using. That's not unusual. Digital devices can be pretty noisy in the radio spectrum.
Are you using an external antenna or the one built into the tuner?
If you are using the tuner's internal antenna, one solution might be to use an external antenna located away from your equipment stand and connect the antenna to the tuner with TV coax cable. (The antenna doesn't have to be outside. 5 or 10 feet from the CD player would likely be more than adequate.)
Tuners are designed to reject a certain amount of noise at the same frequency as the broadcast frequency but there is a limit.
If the external antenna doesn't help, your only other likely solution is to place the tuner itself away from the CD player.
Are you using an external antenna or the one built into the tuner?
If you are using the tuner's internal antenna, one solution might be to use an external antenna located away from your equipment stand and connect the antenna to the tuner with TV coax cable. (The antenna doesn't have to be outside. 5 or 10 feet from the CD player would likely be more than adequate.)
Tuners are designed to reject a certain amount of noise at the same frequency as the broadcast frequency but there is a limit.
If the external antenna doesn't help, your only other likely solution is to place the tuner itself away from the CD player.