Arsenal's Bergkamp, Manchester United's Ronaldo and Liverpool's Fowler all won it twice in a row without managing a hat-trick.
Kane, 21, has already scored twice in March, his double last weekend bringing a 2-1 victory against Queens Park Rangers and giving him 26 goals in all competitions for the season.
"To make history would be something very special," he told Sky Sports News. "Obviously I’ve scored a couple so far this month, so hopefully I’ll get a few more goals and we’ll see what happens."
Later this month Kane is also hoping to earn a first call-up for England, who play Lithuania in a European Championship qualifier on March 27.
"He works very hard in training, his potential is massive and he can improve more," Spurs manager Mauricio Pochettino said.
Pochettino was speaking ahead of Sunday's away game against Manchester United, which could have a crucial bearing on who qualifies for next season's Champions League.
United are fourth, three points ahead of sixth-placed Tottenham.
"We believe we can win," the Argentine said. "You never think before a game that it is possible to lose. You are always focussing on getting the three points and are never thinking about losing.
"Maybe Manchester United has history, but our mentality is to compete and try to win the game."
(Reporting By Steve Tongue; editing by Toby Davis)
Share
