Index: src/js/_enqueues/lib/link.js
===================================================================
--- src/js/_enqueues/lib/link.js	(revision 43640)
+++ src/js/_enqueues/lib/link.js	(working copy)
@@ -508,8 +508,8 @@
 		searchInternalLinks: function() {
 			var waiting,
 				search = inputs.search.val() || '';
-
-			if ( search.length > 2 ) {
+			var serchLength =  parseInt( wpLinkL10n.minimumWordLengthForSearch, 10 );
+			if ( search.length >= serchLength ) {
 				rivers.recent.hide();
 				rivers.search.show();
 
Index: src/wp-includes/script-loader.php
===================================================================
--- src/wp-includes/script-loader.php	(revision 43640)
+++ src/wp-includes/script-loader.php	(working copy)
@@ -589,17 +589,28 @@
 	$scripts->add( 'admin-bar', "/wp-includes/js/admin-bar$suffix.js", array(), false, 1 );
 
 	$scripts->add( 'wplink', "/wp-includes/js/wplink$suffix.js", array( 'jquery', 'wp-a11y' ), false, 1 );
+
+	/* translators: Input word length for incremental post search. Start searching from the number. */
+	$minimum_word_length_for_search = _x( '3', 'minimum length for searching links' );
+	if ( ! empty( $minimum_word_length_for_search ) && is_numeric( $minimum_word_length_for_search ) ) {
+		$minimum_word_length_for_search = absint( $minimum_word_length_for_search );
+	}
+	else {
+		$minimum_word_length_for_search = 3;
+	}
+
 	did_action( 'init' ) && $scripts->localize(
 		'wplink',
 		'wpLinkL10n',
 		array(
-			'title'          => __( 'Insert/edit link' ),
-			'update'         => __( 'Update' ),
-			'save'           => __( 'Add Link' ),
-			'noTitle'        => __( '(no title)' ),
-			'noMatchesFound' => __( 'No results found.' ),
-			'linkSelected'   => __( 'Link selected.' ),
-			'linkInserted'   => __( 'Link inserted.' ),
+			'title'                      => __( 'Insert/edit link' ),
+			'update'                     => __( 'Update' ),
+			'save'                       => __( 'Add Link' ),
+			'noTitle'                    => __( '(no title)' ),
+			'noMatchesFound'             => __( 'No results found.' ),
+			'linkSelected'               => __( 'Link selected.' ),
+			'linkInserted'               => __( 'Link inserted.' ),
+			'minimumWordLengthForSearch' => $minimum_word_length_for_search,
 		)
 	);