Pre- output impedance for ss input impedance 10K

My solid state power amplifier has input impedance 10 KOhms.
I'm searching for a tube preamplifier with the lower possible output impedance. I've asked some top manufacturers about the matching and received totally opposite answers. For example I've been advised not to try a pre with output impedance of 600 Ohms and strongly assured to take a pre with output impedance of 1K.
Does the specific design of the pre- influence this matching, is there another to pay attention to?
Thank you.
I have had this situation, and the common general rule of thumb is for the "maximum" output impedance of your preamp to be no greater than one-tenth the input impedance of your amp, or in your case 1,000 ohms. However, please note two things;
1. that is a "maximum" output impedance. I personally had much better luck considering a ratio of more like 20 to 1, or better, and
2. many tube preamps use coupling capacitors, which have a finite size and can cause an increase in output impedance at lower frequencies. However, output impedance is often spec'ed at 1K ohms, so some research may be necessary to determine if that is so. For example, the output impedances of both the Aesthetix Calypso and Lamm LL2 increase to over 3K ohms at lower frequencies. This would cause some level of low bass roll off with your amp. How this affects you will depend on some other things, and may not be an issue at all if you do not have almost full-range speakers. I suggest reading the "Measurements" section in the Stereophile reviews of the preamps you are interested in.
vtl-6.5, Nagra, sonic frontiers line 2 or 3
You want the lower output impedance pre - this will work best. I agree with Mitch.