Not disposed to marry; not matrimonially inclined.
The Century Dictionary (Public Domain)
Use "non-marrying" in a sentence
"Let's talk about the non-marrying man for just a moment."
"She was in no mood for the barren blossom of non-marrying men's compliments."
"Therefore he had been set down as a non-marrying man -- "an awfully good fellow, but with queer ideas, you know," his many friends would say, and "Bully""