Kane's league-leading 22 goals, three more than Leicester City's Jamie Vardy, have kept Tottenham in the hunt for the title and have made him a virtual certainty to lead England's attack at the European Championship in France in June.
"I'm simply amazed how consistent Harry, at still such a young age, performs week in week out," former Spurs striker Klinsmann told the club's website (www.tottenhamhotspur.com).
"His composure with the ball, his vision for his team mates, his decision-making, is almost always spot on," added the United States coach.
Kane's five goals in March earned him the league's Player of the Month prize on Friday and he was also on target in the 1-1 draw at Liverpool last weekend.
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After scoring 21 league goals last season, Kane's slow start to this campaign prompted doubts about his ability to cope with raised expectations.
His stunning form since, however, has underlined the striker's transformation from a player with raw potential to one of Europe's most lethal goalscorers.
Another admirer is Teddy Sheringham, the former Tottenham, Manchester United and England forward who Kane has often been compared with.
Sheringham, scorer of 146 Premier League goals, said Kane's versatility was his biggest asset.
"I like that he's not just one particular type of striker," said Sheringham who was born just a few miles from Kane in east London.
"He can run in behind, he can hold the ball up, win it in the air, drop off, lay people in, has lovely touch, finesse and vision and sees other players around him.
"For me he's got everything."
Kane himself wants to add to his club record 22 goals in a Premier League season, starting this Sunday when second-placed Tottenham host Manchester United who are fifth.
Tottenham are seven points behind Leicester with six games to play and need a storming end to the season to have any chance of overhauling the leaders.
"We're just taking it game by game," said Kane. "With Leicester being top we're the ones who have to keep putting the pressure on and making them slip up, that's all we can do."
(Reporting by Martyn Herman)
