In order to display an input field for Users, in a visualforce page, OwnerId field should be writeable. Unless your field security permissions are messed up or for example, the field is hidden because it's a detail in Master-Detail relationship.
But when you'll manage to get it to work you'll see that most likely it's a bit weird lookup that can point to User or Queue.
If you're fine with that - great, just check the security around the field. If you need really only a lookup to a user - check if you have any custom Lookup(User) field? You could create a dummy record of that type in the controller and don't do any DML with it, just use the fact it'll have the lookup.
If you don't have any custom ones - I think that Account / Contact / Opportunity owner must be a user (can't have queues). You might have to force <apex:input field... required="false"/> but other than that it should OK?
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