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.
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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.
“Sometimes there is things you want to talk about, you might have personal problems but you feel uncomfortable going to the manager but with Steven you can go and talk to him about anything. He is chilled.
“He reminds me of Harry (Redknapp) and Sam Allardyce where you can approach them and speak about anything. It is important.”
Gerrard’s career, in common with much football around the world, is currently on hold with the Scottish Premiership one of several leagues that have been suspended in response to the coronavirus outbreak.
But Defoe, capped 57 times by England, had no complaints about the move given the spread of COVID-19.
“To be honest, there are more important things happening in the world than football,” he told TalkSport.
“People are dying every day which is such a sad thing, it puts things into perspective and you think, you know what, football is not important at all at this moment in time.”