Can't give gifts to some villagers?

[Sir Zyr]

So, I'm confused. There are two villagers in my town (Admiral and Ankha) where the option to give them a gift when talking to them never shows up. This is annoying because there are gifts that I want to give the two of them. (Others do lack the option sometimes, usually when they're sitting down or working on something)

does anyone have any idea why these options aren't showing up for these two villagers?

 

[ForgottenT]

In my experience I've had to be good friends with the villager before the option shows up.
But you can just mail them the presents.

 

[meo]

There's an intro phase with newer villagers where you can't gift them via chatting. You have to talk to them over the span of a few days or so to develop a relationship.
It will unlock, just got to have patience. Keep talking to them daily.