Support for formal KM should be top down as there will be the need for an eventual spread of knowledge workers across the organization, not just within the PMO. Ideally, there is a separate KM group which will drive processes and practices. A Community of Practice will begin to create a collective of 'advocates' across the organization's departments.
That said, you could certainly spearhead a KM initiative. It has to start somewhere. With a solid plan and strategy, the PMO can help drive the importance of KM practices, exposing the value to the organization through results.