I had a very similar situation a while ago. 125 kHz, not 10 kHz. Spent days looking for the culprit.
It wasn't until I moved the equipment that I realised it was only present in that one spot in the room. Turned out the culprit was a VFD driving the big sewer pumps under the road.
I've moved my equipment to another spot in the room. No more problems.
It made me curious and I found two other spots in the house where the same interference is present. Both are 3-phase circuits that are no longer used. The first one, however, has not 3-phase circuit near. At least, as far as I can tell.
Even my Fluke DMM behaved strange in that spot. Showing up to 6-7 volts on the DC range, with the leads attached to nothing.