That is quite a problem, especially since the product owner should ideally be someone with a vested interest in the product, which sort of implies that you cannot use a consultant as a ersatz product owner. Unless you intend to keep the consultant on for basically forever.
I has the luxury of working with a good product owner once. We recruited him for the task at hand, so he had no background in the organization doing nothing other than his PO duties. This turned out to be a great boon, and managed to avoid the usual pitfalls of developer-turned-PO or boss-also-doing-PO.