The former Spurs striker also believes Kane is better than Chelsea forward Diego Costa.
The former Spurs forward told TalkSport he thinks Kane is the complete number nine, able to dominant the front line from a high position or sitting deeper.
Tottenham's Harry Kane celebrates scoring their third goal
Kane scored his first hat-trick for Tottenham against West Bromwich Albion at the weekend, as Mauricio Pochettino's men climb to second spot in the Premier League table - seven points off leaders Chelsea.
Former Republic of Ireland international Keane scored 91 goals in North London for the Lily Whites over a two-spell eight year career. Having seen the development of Kane, the Irishman now firmly believes he could become a league legend.
Robbie Keane after signing for Tottenham
Keane told the Jim White Show: "Harry Kane is a proper striker. He can play high up, he can come deep and get on the ball.
Ultimately, you are judged on scoring goals and he is scoring a lot of goals."
Having broken into the Tottenham first team in April 2014, Harry Kane has notched 20+ goals in each of the last two seasons. His triple against the Baggies at White Hart Lane was his 13th of the campaign - just seven short of another similar haul in mid-Janaury.
Tottenham Hotspur's Harry Kane wins the 2015/16 Barclays Golden Boot Award, scoring 25 goals.
Making his 100th appearance against Watford on New Years' Day, the 23 year-old won the Premier League golden boot for his 25 goals last term.
Kane is one behind Chelsea striker Diego Costa for the season, but nevertheless Robbie Keane believes the Englishman is more complete striker than the Brazilian-born Spaniard.
"If you say Diego Costa is world class, what is the difference between him and Harry?", posed Keane.
"They score a similar amount of goals. I think in the next few years Harry could go on to become an all-time great in the Premier League. He is certainly on his way."
Have something to tell us about this article?