A bit of background

• NuxtJS (build as static) is a client side app.
• WordPress is a PHP server side app
• A wordpress site usually get served to users by web servers like apache or nginx.
• Client side apps served by any web server (including apache or nginx)

So you can't "deploy wordpress in nuxt", but it is simple to get what you want:

1. Follow this guide to move the wordpress to a subdirectory
2. Upload the nuxt app to the root directory

In case you are using SSR or any other requirements that force you to use Nuxt in server mode, your options are:

• Setup nginx as reverse proxy
• Setup apache as reverse proxy
• Setup a proxy in the node server itself, maybe this project could help

I think there may be a problem with this without the wordpress API, but the question is, do you care about Nuxt.js or maybe just Vue is enough? Remember that in Vue 2 you can use an inline-template, thanks to which you can render elements on the server side. For this you will add the necessary elements from the Vue ecosystem, such as a router and setup you will have similar to Nuxt.js. Example code:

<div is="navbar-dropdown" inline-template>
    <div v-cloak :class="isOpenDropdown ? 'visible opacity-1 mt-0' : 'invisible opacity-0 mt-10'">
        <?php get_search_form(); ?>
    </div>
</div>