Mikoto to Hayate: "You look a lot like the man who shamelessy married someone important to me".
Implying that with "someone important" she meant Yukariko, then I can assume that Hayate may be
a son of Shin Hayek (Nagi's father), from a different woman maybe?
I mean, this old image was pretty daring already.
Not to mention, short after the sentence I quoted in the beginning, Mikoto adds "And it would seem blood is powerful, you're even a butler". Shin was Yukariko's butler.