I say this out loud all the time but it’s usually always towards my husband who died last year as I miss him terribly.
Ironically, finding and reading your post..I made the apparently BIG mistake of saying I miss you to someone just the other day. We had developed a close friendship, so I thought, and while we were having a lovely text conversation, I uttered those three words ‘I miss you’. I missed his company and his presence right then, in that moment, and without thinking I said it.
I expected nothing in return except an ‘I miss you too’ The outcome from that comment was something quite different. He managed to twist and turn something meant to be so simple and sweet into something else entirely. It went weird fast and my feelings got hurt. However, I’ve learned that you can’t help how the minds or others work and you have no control over how they perceive you, no matter how truthful, authentic and honest you are with them. Miscommunication and misunderstanding sucks.

Something funny happens (or you read something amusing) and you look around and there is no one with whom to share it...
You go days/weeks/month without so much as a hug from another human...
You reminisce about regrets....paths you wish you had taken year ago...

You can easily miss the you that you used to be....and you can also miss having a companion with who to share the current path....

It's actually very common to "miss" having someone without knowing if it's just our previous selves we miss...or an unknown person we wish we had met....or someone real from our past.

I personally miss the "me" I used to be...and I miss my all my doggie daughters and sons....and I miss having just one person in my life who truly put me above all others....

There are two people that I say this phrase about. Never do I not know who I am missing.

I will have other stuff come through sometimes... most often imaginary conversations will pick up steam until I start gesturing and muttering some of the words. I don’t think that’s exactly what your talking about... but I have had people say “what are you doing?” every once in awhile... when I didn’t realize I was starting to play out the internal dialogue... usually while doing some mindless task (driving, painting, etc.) that leaves my brain free to wander.

Oh! I do sometimes have random names intrude... for whatever reason, my brain will start repeating a name over and over again through the day, sometimes longer... most often I think it is just the sounds of the phonemes that some part of my mind latches on too. It doesn’t seem to have to do with who the person is. Ricardo Montalban.... Ricardo Montalban... ha ha ha

The phenomena you describe is pretty evocative. It reminds me of studies with patients who have had brain hemispheres separated... both hemispheres still function, but the right hemisphere no longer has access to the left hemisphere speech centers so it has to find other ways to express itself, drawing, behaviors, etc... it still “speaks” but the meaning has to leak through in some other way. Sometimes the two hemispheres will totally contradict each other. In many ways, we are at least two people. Perhaps some part of you that has a hard time finding a voice, maybe even a voice you actively suppress, is attempting to convey something.

If I were to guess... I’d just go for the low hanging fruit. You’re lonely. It is after all a “someone” that you are missing. Maybe the reason you don’t know who it is that you are missing is because you haven’t met them yet. We are often cautioned not to seek completion in the form of another person, and perhaps that is the part of you that is suppressing or at least avoiding the more obvious interpretation of the words. Maybe you just miss missing someone? Was that something that occurred frequently in former relations? Maybe it’s just an emotional pattern that’s comfortable for you as vestige of a former relationship?

...just thoughts...

Maybe your mind is trying to tell you something.

I don't know though as this has never happened to me.