Do you know the paper <a href="http://www-irma.u-strasbg.fr/~loday/PAPERS/98LodayPira%28linmaps%29.pdf">of Loday and Pirashvili</a>? They discuss what, in their opinion, should replace the notion of a Hopf algebra in Leibniz setting, "Hopf algebras in the category of linear maps".