Defoe started the season nursing a groin problem but he was in sublime touch for England when he injured his ankle, just days after his Wembley hat-trick against Bulgaria. For his club, however, his own prolific standards have slipped recently and he has only four Premier League goals in 2010.
"Jermain can actually score more goals than he does," said Redknapp. "He should get 20 goals plus every year. Last season he had an unbelievable spell and then he dried up.
"I told him, 'It's wrong if you don't get 20 goals a year'. I tipped him to be leading scorer in the Premier League and I told him it was about time he did it. It's up to Jermain to try to emulate the greats."
When Redknapp talks of the greats in front of goal, he is thinking specifically of Jimmy Greaves.
"Greavsie was the best, a genius," said the Spurs boss, but he believes Defoe also boasts the single-minded instinct of a true poacher. "They get in front of goal and they're cool. They don't panic and they pick their spot. Greavsie was like that. And Gary Lineker.
"Even when the team's getting beat, you still get the feeling they will score so they can say, 'Well, I've scored'. That's the way they are.
Redknapp and Defoe have worked together at West Ham, Portsmouth and Tottenham and it is probably the closeness of their working relationship which persuades the manager to expect such high standards from the 28-year-old.
"His goalscoring and his movement is fantastic but I still think there's part of his game he can improve. To be the complete front man, his hold-up play can be better. When the ball comes in to him, he can be stronger and protect it better."