Totti, who remained with the Serie A side throughout his career, led Roma to a top-flight title in 2001, before winning the World Cup with Italy in 2006.
England international Kane, who said that he watched his fellow striker growing up, has lauded Totti's achievements in the game.
"He was a fantastic player and to spend your career at one club is an amazing achievement," Kane told reporters.
"He achieved everything he wanted to at that club. He is a fantastic striker and, growing up, I would watch his goals.
"He had a brilliant career and, hopefully, I can have the same."