Read more at: https://blogprime.com/enable-dns-prefetch-in-wordpress/

functions.php

<?php

/* Please don't copy the opening <?php tag */
function blogprime_homepage_dns_prefetch() {
  /* variable for storing the homepage url */
  $homepage = get_home_url();
  /* variable for storing the next post url */
  $next_post = get_next_post();
  /* variable for storing the previous post url */
  $prev_post = get_previous_post();
  /* if homepage is present (not empty) then do following */
  if ( !empty( $homepage ) ) {
    echo '<link rel="prefetch" href="'.$homepage.'" />
      <link rel="prerender" href="'.$homepage.'" />';
  }
  /* if next post is present then do following */
  if ( !empty( $next_post ) ) {
    echo '<link rel="prefetch" href="'.get_permalink( $next_post->ID ).'" />
      <link rel="prerender" href="'.get_permalink( $next_post->ID ).'" />';
  }
  /* if previous post is present then do following */
  if ( !empty( $prev_post ) ) {
    echo '<link rel="prefetch" href="'.get_permalink( $prev_post->ID ).'" />
      <link rel="prerender" href="'.get_permalink( $prev_post->ID ).'" />';
  }
}
add_action( 'wp_head', 'blogprime_homepage_dns_prefetch', 10 );