Kane took his season tally to 30 goals in all competitions last weekend, while the England international striker is the Premier League's joint-top goalscorer with 20 alongside Chelsea's Diego Costa.
The 21-year-old's goals have helped Tottenham contend for the UEFA Champions League spots this season, though their hopes have faded recently, with Mauricio Tottenham's men occupying sixth position behind Liverpool on goal difference.
Tottenham's standing in the league table would not have been possible without Kane, according to Phillips, who was the last Englishman to net 30 Premier League goals in a campaign with Sunderland back in 1999-00.
Phillips congratulated Kane on his breakout season but said said it was too early to start comparing the youngster to some of the country's greats.
"I would love to see Harry go on and win it, and good luck to him - although I think it's going to be difficult for anyone else to win the European Golden Boot when Ronaldo and Messi are around," the 41-year-old told The Mirror.
"Now the big question is whether he can keep it up. In 1999-2000, I scored 30 goals in the Premier League and the following year I was called a failure when I scored 18, which I thought was very harsh.
"To score 18 goals a season in any major league now is a success. I don't think Harry needs to score 20 goals next year not to be called a failure because times have changed.
"But he's had an outstanding season, he's been fantastic, and he's done it the hard way - because speaking to the people at Leicester, he wasn't a great success when he came here on loan.
"He's been incredible, especially with the pressure at a big club like Tottenham. He's carried them this year - without Harry's goals, they may only have been mid-table.
"When I look at young strikers coming through, he is the future of English football. But the next Alan Shearer, as some people are talking?
"Let's not get too carried away, let's see what happens next year."
