The two-time Premier League Golden Boot winner is already top of the goal chart this season with eight strikes in the English top flight and 13 in 12 in all competitions for Spurs.
Kane has been linked with a move to Madrid and has not ruled it out, but it has been reported that Tottenham will demand £200 million for him.
Ronaldo won FIFA's The Best Player award for the second time in a row last week, but Freund believes it is the England star who is already No.1 in some respects.
"Kane can be Cristiano Ronaldo's successor," the former Spurs player told Sport Bild. "He has had an incredible development and gets better every season.
"Passing, heading, shooting technique, dribbling, finishing, while Harry is not perfect, in any of these areas, he can do something exceptional and has no weaknesses at all. That makes him the most complete striker in the world.
"He carries Tottenham with his heart. But Harry is a thoroughbred professional and always wants the maximum success."
Kane, who is contracted to Tottenham until 2022, is likely to line up in Wednesday's Champions League game against Madrid after missing Saturday's 1-0 defeat to Manchester United due to a hamstring inury.
With the two sides tied at the top of Group H with seven points from three games, coach Mauricio Pochettino remains optimistic that his key player will feature.
"We are really confident," Pochettino told a news conference.
"It may be possible but I don't want to say 100 per cent as we have one more day.
"He trained today but it is important we make the right decision."