The 68-year-old, who spent four years at White Hart Lane between 2008 and 2012, believes the young Englishman can replicate his form from the previous campaign; during which he scored 31 goals in 52 appearances across all competitions.
Writing in his column for the London Evening Standard, he said the following:
"Harry Kane will have another great season because he is a smashing lad with the right attitude but Tottenham need another front man alongside him because he can’t keep doing it on his own.
"It will be hard to replicate last season when he scored 21 goals but he is well grounded, well brought up and knows he has to work hard to succeed. He is a not a big head now he’s had some success."
Clearly the the former Spurs manager agrees with the consensus - Tottenham need to add another striker to their ranks before the close of the summer transfer window.
West Bromwich Albion striker Saido Berahino (Mirror) has been linked with a switch to White Hart Lane in recent weeks, as has Queens Park Rangers' Charlie Austin (Mirror) and Lyon's Clinton N'Jie (talkSPORT).
However, currently there does not appear to have been a breakthrough with any of these reported moves, which leaves the Lilywhites with just Kane to reply on up front ahead of the club's opening weekend visit to Old Trafford.
Redknapp clearly appreciated that signing a prolific striker is easier said than done, but he suggests it is almost a necessity if Spurs wish to climb the Premier League table.
"I like Mauricio Pochettino a lot but he needs the tools to get Spurs up the table," he continued.
"Top-class strikers are hard to come by but to rely on Kane alone to get Tottenham in the top four would be a huge gamble. They need two or three players before the window closes."