I don't think were going to see much of her engaging in any type of training.
OP said the future. Plus she should be old enough to be a shinobi in Part 3 (the movie) - Considering her brother was 3-5 when she was a toddler, she should be learning the basics right about now.
I like the tought of her being trained by her gramps (Hiashi) personally, but having Kurenai/Asuma's daughter as her oficial sensei...