se_plugin_has_update.php

<?php
add_action('admin_init', function() { 

	// Specify here the plugin name and that's all
	$requested_name = 'AJAX File Upload';
	
	function se_plugin_has_update( $name ) {

		if ( ! function_exists( 'get_plugin_updates' ) ) {
			require_once ABSPATH . 'wp-admin/includes/update.php';
			require_once ABSPATH . 'wp-admin/includes/plugin.php';
		}

		$list = get_plugin_updates();
		$data = array();

		foreach( $list as $i => $item ) {	
			if( strtolower( $name ) == strtolower( $item->Name ) ) {
				$data = $list[$i];
			}
		}

		if( ! empty( $data ) ) {

			$data = array(
				'name' => $data->Name,
				'version' => $data->Version,
				'new_version' => $data->update->new_version,
				'url' => $data->update->url,
				'package' => $data->update->package
			);

		} else {
			$data = array();
		}

		return $data;

	}

	$update_data = se_plugin_has_update( $requested_name );

	// var_dump( $update_data ) or print_r( $update_data ) for debugging

	if( ! empty( $update_data ) ) { // has update avail

		// You can avoid for specific versions (current: $update_data['version'] and latest: $update_data['new_version'])

		$GLOBALS['se_plugin_has_update_data'] = $update_data;
		
		add_action( 'admin_notices', function() {

			global $se_plugin_has_update_data;
			$update_data = $se_plugin_has_update_data;

			?>
			
				<div id="updated" class="error notice is-dismissible">
					<p><?php echo sprintf(
						"\"%s\" plugin has updates available. You are running v. %s while the latest version is %s",
						$update_data['name'],
						$update_data['version'],
						$update_data['new_version']
					); ?></p>
				</div>
			
			<?php
		});

	}

});