Sony CDP-337ESD clicking noise

Hello everyone!
I have bought a Sony CDP-337ESD player, everything is fine except clicking, ticking noise when the disk is rotating.
I made a recording of it, here is the youtube link: Video
This noise seems to come from the clamping mechanism or the motor but not sure.
When I push a little bit down the clamper when playing a CD, the noise stops: Video

Do you have any idea what to check and do to eliminate this problem?
It is such a nice player (design, sound), it would be a shame if I could not do anything to solve it.
 
It is likely to be a mechanical noise from the focus coils that support the laser assembly. If you listen carefully, you can here the slight rasping sound of the focus or maybe tracking coils as the laser searches the disc whilst playing.
If it were a turntable motor issue, I would think that it would have trouble reaching the speed required tp read the TOC at the centre of the disc.
This is purely guess work as I am not working on it.
 
The laser suspension is sagging and the focus offset has changed. Theres really nothing you can do other than replacing the optical PU asy and recalibrating it, but then you run the risk of worse tracking performance thanks to the age of all these PUs having sat on the shelf for the past 35 yrs. I personally would just live with it. I have a few CDPs with KSS240A PUs and they all do what you describe to some degree.

The single beam Philips based players usually track much better anyways, which is why I use one as a transport, especially with scratched CDs. None of my Sony PU based players come close. Its a shame because I have an NEC with dual differential TDA1541As that sounds amazing but the Sony PU they used sucks in comparison.
 
I think is the round piece that attach the cd to de spin motor, that graze or touch the superior arm where is housed. It is a very little tiny graze, but is audible. Move the superior arm to the left or right to see if I'm right or wrong.