Native speakers never omit the preposition between reply and [recipient]. From Google Books...

[We haven't] replied to him yet (868 hits) [We haven't] replied him yet (2 hits - but actually they're probably duplicates anyway)

Looking more closely at the second instance(s), I think there's strong evidence to suggest the writer isn't even a native speaker of English anyway.

In such contexts, reply (as with similar words such as respond, react) normally requires the preposition to if a recipient is explicitly specified - unlike, say, answer or tell, which don't normally have a preposition between verb and patient (patient = object of an action = the person replied to).

Another common "object" of the verb reply is the noun "reply" (the text of the reply itself). That's to say...

"This is the answer" replied John. which could be resequenced as John replied "This is the answer".

is what's called "transitive" usage. The conventional definition of a transitive verb is a verb that requires one or more objects, but I'm not sure that's particularly helpful here. It makes more sense to me to say...

The verb reply can either be used intransitively (i.e. - with no "object"), or with one or both of two types of object - the response itself (no preposition) and/or the person addressed (preceded by to).