Can a CD player being close to a receiver or power amplifier affect its performance?

Wrap the digital player in copper mesh sheets to make a faraday cage around it. Will stop any digital hash from affecting your other gear. Cheap too. Fold and solder the seams. Crimp or folded seams don’t really work that well. 
I’m make a habit of doing this with all my digital stuff that isn’t already shielded, and with any shielded cables carrying digital signals; along with outbound switching power supplies, their power cords and output cables.

It’s really surprising how it will quiet down your system. 

EMF interference follows the inverse square law -- doubling the distance of empty space between two pieces of equipment reduces the interference to one-fourth of what it was before. Therefore, if that was the problem, often a small increase in separation fixes things.

Heat can also be an issue, but you'd likely notice the increased warmth if that was the issue.

Maxwell suggests all things transmit and receive...