Although Vetinari seems to express little interest in women (or men for that matter) we do know that in his youth he had something of a relationship with the Lady Margolotta of Uberwald.
On the face of it, it appears that their relationship was not sexual, but that he would have liked it to have been:
“Oh, in my younger days I spent some time in Uberwald,” said the
Patrician. “In those days rich young men from Ankh-Morpork used to go
on what we called the Grand Sneer, visiting far-flung countries and
cities in order to see at first hand how inferior they were. Or so it
seemed, at any rate. Oh yes…I spent some time in Uberwald…”
It was not often Leonard of Quirm paid attention to what people around
him were doing, but he saw the faraway look in Lord Vetinari’s eye.
“You have fond memories, my lord?” he ventured.
“Hmm? Oh…she was a very…unusual lady but, alas, rather…older than me,”
said Vetinari. “Much older, I have to say. But…it was a long time ago.
Life teaches us its small lessons, and we move on. The world changes.”
There was the distant look again. “Well, well, well…”
Ankh-Morpork's increasing involvement in the politics of Uberwald seems to have rekindled their friendship. in Unseen Academicals, his relationship with the "Dark Lady" has even become something of an open secret among the gentry. Obviously no-one's quite sure what's actually going on between them but I suspect they're jolly pleased that he isn't into anything weird...
Lady Margolotta was behind all that. She was the person who, by
diplomacy, and probably more direct means, had got things moving again
in Uberwald, and she had some sort of…relationship with Vetinari.
Everyone knew it, and that was all everyone knew. A dot dot dot
relationship. One of those. And nobody had been able to join up the