In this study, we propose an extremum-seeking control approach for the design on nonlinear observers for a general class of detectable nonlinear systems. The extremum-seeking control approach provides a mechanism to compute an observer gain that minimizes the squared output error. The technique extends and generalizes an earlier extremum seeking control observer design approach that was limited to systems in observer normal form with a linear state to output map. The analysis provides conditions for the application of the technique and establishes a semi-global practical stability property of the error dynamics. Two simulation examples are presented to demonstrate the effectiveness of the technique