At 37 Defoe is nearing the end of a career that has seen the forward work with the likes of managers Harry Redknapp and Sam Allardyce during spells at several clubs, including West Ham, Tottenham, Portsmouth and Sunderland.
Defoe compared Gerrard, in only his second season as a manager, to both Redknapp and Allardyce, adding the former Liverpool and England captain had a similarly acute understanding of players.
"I think he is going to be a top, top, top manager," Defoe told Talksport radio.
"He is brilliant, he is a natural. In terms of management he is still fresh and new but you can see that naturally he has got everything. He always says to the players that if they want to go and talk to him his door is open. He is approachable which is really important as a manager".