If Rei wasn’t as indifferent towards Asuka as she was and warmed up to her a bit I don’t see why they couldn’t have formed a bond. I wish so as well. I think that throughout the EoTV Rei and Asuka never really able to form that connection. I think it was mostly because Asuka had been quite envious ...

I suppose the mother becoming sort of crazy is the trigger point which changed Asuka.