There is a theory going round that his father was Aerys the mad king. We know that John Sner is a Targ, and the dragon liked him and let him stroke his nose. But Tyrion was able to touch them too, when he released the two from the pyramid.
This is quite an old theory. There's stuff in the books about how Tyrion's eyes are almost violet as well - which is well Targey.
And there was mention of the fact that Aerys liked to take liberties with Joanna Lannister and complained that her boobs had sagged since having the twins.