What is the most analog sounding CD player under $

What is the most analog sounding CD player under $1000 new or used?? I am not talking about a overly warm and mushy sound. Just a natural detailed sound that would remind one of vinyl. Thanks,keith
i was very impressed with the vincent s1.1, which is a hybrid tube player--very natural sounding. they also make tubed players (probably available used at your 1k target) which are well worth checking out.
Meridian 508.24 is one to consider

Perhaps a Rega Apollo?

I have a Rega Saturn which is absolutely wonderful - detailed, neutral, and smooth. You might be able to find one for around $1k used. New price is about $2,500.

The Apollo costs $1k brand new. By reputation it is a little warmer and more analog sounding than the Saturn, though possibly less detailed than its more expensive sibling.

Rega's digital equipment has a reputation for sounding more analog than most.
The Rega is wonderful. I'm not sure I'd call it "analog" sounding. Very realistic and detailed. If you want to warm it up, there are good tubed models out there such as the Raysonic 128 or the Shanling 3000.
Yoiu might like California Audio Labs. They made fantastic CD players. I still prefer mine to this day. I may take the plunge just to get into the newer formats but the Cal's sound great. They can be had most of the time under $500.
The Meridian is hard to beat for the money and performance. Can be a bit tempermental with reading discs sometimes.
This Resolution Audio CD-50fits your requirements. I don't know the seller but do own one. Yeah we all recommend the item we own bur I've had mine for years now. Can't find better, and I have tried.
Sony XA5400es
Like a modern CD Player/Turntable
Would the 5400 be much different then the SCD XA777ES?? keith
PrimaLuna Prologue 8 with upgraded circuit
Try the Vincent Audio tube cd player, very analog sounding and within your price range used. The hard part is finding it used though. I owned it for 3 years so I'm very familiar.
5400 is more refined with better frequency balance in my opinion.
All excellent suggestions.
You got a lot of good suggestions but I question the premise of your original comparison question. I've owned a few different turntables and CD players over the years and I've had CD players that sounded more "analog", or in general much better than some of my turntable/cartridge combinations. Sorry, don't mean to derail this conversation but I'd like to hear someone explain what "analog sound" sounds like.
without getting involved in the analog v. digital debate, I think when people talk about an analog-sounding cd player, they mean something on the warmer side.  
Yamaha CD-S1000  The mellow sound of the BurrBrown dacs sound more analog like.  
I found it! In an antique shop covered with rust and gunk.  The transport had to be prodded with an ice pick to get the tray to open.  The CDs skip, distort, and the music can barely be heard underneath the cacophony of debris.  Just like vinyl!
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If you want 'analog' sound from digital---get isolation for your digital and preamp. Simple eh? (Canadian eh). Otherwise it does not exist. Seriously.
What do you mean by isolation - physically or electrically? To the OP, I'm also in the same situation as you and have decided to look for a better DAC than a "better" CDP. I think that approach provides a better longer term path for future growth.