The England international ended his goal drought with two goals in Tottenham’s 3-0 win against Everton at Goodison Park in their Premier League opener.
Spurs forward Kane failed to get on the score sheet in the north London side’s opening three Premier League games to continue his poor record in August.
The 24-year-old scored 29 goals in 33 fixtures in the Premier League last season to finish as the division’s top goal-scorer ahead of Everton striker Romelu Lukaku.
Kane has netted 101 goals in a mere 169 appearances in the Premier League to reach the 100-goal milestone faster than Arsenal legend Thierry Henry.
Liverpool have struggled to sign a centre-forward capable of scoring 20 plus goals a season since Luis Suarez was sold to Barcelona in a £65m deal in 2014 summer transfer window.
Former Liverpool defender Carragher admitted that he would love to sign England and Tottenham striker Kane ahead of any other Premier League player.
“He may not be the best player in the Premier League, though he wouldn’t be far off. He’d be in the top bracket,” Carragher told Sky Sports.
“But if I was a manager and I could pick one player from the Premier League in my team, I’d pick Harry Kane because I think he’s an absolute guarantee every season of 25 goals.
“Over a four or five year period he’ll be getting another hundred and he looks very strong mentally.
“He looks as if the only thing he focuses on is football and he doesn’t get involved in any other nonsense.
“He’s in the top class.”
Liverpool lost 5-0 to title rivals Manchester City at the Etihad Stadium last weekend to cast double on their title challenge.
Tottenham, meanwhile, were 3-0 winners at Everton in their fourth Premier League game.
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