No.

Tom's /Voldemort's whole thing is extinguishing Muggleborns, half-bloods (even though he was one himself), people of the Muggle kind and those he deemed "blood-traitors"

Why would he, of all people want to engage in a relationship, romantic or otherwise, with a Muggle-born?

Answer:
He wouldn't.

Canonically speaking, he wouldn't

And isn't there a conspiracy in which people theorise that he (Tom or Voldemort, Voldemort or Tom), was unable to feel love as he was conceived using a love potion / under the influence of a love potion

I'm not quite sure whether or not it has been confirmed, because as I've said, I'm not really in the "fandom" anymore, nor do I keep up with what's supposedly canon now.

And was there not a rumour in which it was stated Voldemort was, in fact, asexual? And yes, I know, asexuals and asexual people can and may have romantic relationships but still, no.

It's not viable.

It's not likely.

It's not going to happen, I'm sorry.

And please, do not remind me of the age gap
Obviously, I know AUs exist but Canonically speaking, aha, no.

Score out of ten:
0.01/10

Probability:
0.01/10 because you never quite know