Summary:
From the information contained in the WordPress Developer Resources I read that it can set the return format https://developer.wordpress.org/cli/commands/core/update/ but give a return only for table format.

Steps to reproduce:
Run command ‘wp core check-update --format=json’

` /**
* Checks for WordPress updates via Version Check API.
*
* Lists the most recent versions when there are updates available,
* or success message when up to date.
*
* ## OPTIONS
*
* [--minor]
* : Compare only the first two parts of the version number.
*
* [--major]
* : Compare only the first part of the version number.
*
* [--force-check]
* : Bypass the transient cache and force a fresh update check.
*
* [--field=]
* : Prints the value of a single field for each update.
*
* [--fields=]
* : Limit the output to specific object fields. Defaults to version,update_type,package_url.
*
* [--format=]
* : Render output in a particular format.
* ---
* default: table
* options:
* - table
* - csv
* - count
* - json
* - yaml
* ---
*
* ## EXAMPLES
*
* $ wp core check-update
* +---------+-------------+-------------------------------------------------------------+
* | version | update_type | package_url |
* +---------+-------------+-------------------------------------------------------------+
* | 4.5.2 | major | https://downloads.wordpress.org/release/wordpress-4.5.2.zip |
* +---------+-------------+-------------------------------------------------------------+
*
* @subcommand check-update
*/
public function check_update( $_, $assoc_args ) {

	$updates = $this->get_updates( $assoc_args );
	if ( $updates ) {
		$updates   = array_reverse( $updates );
		$formatter = new Formatter(
			$assoc_args,
			[ 'version', 'update_type', 'package_url' ]
		);
		$formatter->display_items( $updates );
	} elseif ( empty( $assoc_args['format'] ) || 'table' === $assoc_args['format'] ) {
		WP_CLI::success( 'WordPress is at the latest version.' );
	}
}

`