In this paper, the problem of unknown input observer (UIO) design for nonlinear parameter varying (quasi-LPV) systems is investigated. Three main improvements of the existing UIO designs for LPV systems cite{Marx2019} are detailed. First, the parameter dependency of the UIO is not restricted to be the same as the one of the system, then the existing decoupling conditions are relaxed. Secondly, the class of considered systems is nonlinear which leads to the well-known quasi-LPV systems (i.e. the parameters are state dependent). This paper focuses on the case of parameters depending on unmeasured states. Finally, the proposed UIO considers the cases when only estimated time derivative of the parameters is available, and also unavailable time derivative and estimation. For these cases, the Disturbance-to-Error Stability (DES) is considered with DES-gain optimization. Examples are provided to illustrate the performances of the proposed UIO designs and highlight the improvements brought to existing ones.