A Madrid source said: "Zahavi has been told to do all he can to try to bring Rooney to the Bernabeu. The club are confident a deal can be done."
Speculation about the England striker's future has intensified following revelations about United's precarious finances.
Perez, who signed Cristiano Ronaldo from United in a world-record £80million switch last year, normally gets what he wants.
Employing Zahavi shows Real are serious in their pursuit of Rooney, 24.