Hard to say. Her father could have been a servant. Heck, her father could have been an Elf! We have seen that human trumps everything else genetics wise. Except maybe Qunari.
I think it seems highly likely, and wouldn't be surprised if the writers confirmed Leliana is elf-blooded. Many people have speculated about this, given Leliana's fascination with everything regarding elves, her positive disposition toward an elven Warden (it's no surprise Leliana x Mahariel is probably one of the most popular Leli pairings out there, rivaling Leliana x Cousland).
The fact she supports Briala (an elf) for the throne strengthens this belief further and she is also the best advisor for the Lavellan Inquisitor War Table missions. She seems to be really familiar with elven customs, society and language.
Regarding her parentage, I think her mother was an elf and her father was human. We know her mother was a servant to an Orlesian noblewoman, and that Lady Cecile had more than a few elven servants. (Leliana mentions after her mother's death she was taken care of by an elven servant of Cecile for a while). She seemed to understand elven language and learning their songs even when she was little.
It kinda makes more sense for her mother to have been an elf rather than human when she was a servant in Orlais given elves are more common in that department.