Kane has once again been leading Spurs from the front this season, scoring 20 goals across all competitions, despite the club finding consistent results hard to come by under Jose Mourinho.
Murphy rates Kane as "among the best three strikers in the world", but says he now has a decision to make: chase trophies or break club records at Tottenham - much like Thierry Henry at Arsenal.
"It's a huge summer for Harry Kane," Murphy wrote in his Mail column. "If he doesn't leave Tottenham now, he never will.
"He'll finish as the club's record goalscorer and have a statue built outside the stadium if he stays but at the expense of winning the trophies his talent deserves.
"I’m sure he's thinking about it every day because time isn't on his side. Right now, he is among the best three strikers in the world and would improve any team.
"But he turns 28 this summer, with younger models Erling Haaland and Kylian Mbappe becoming increasingly attractive to the elite clubs every year.
"Kane clearly loves Spurs and wanted to give Jose Mourinho every chance this season. But they are miles off challenging for a Premier League title or Champions League so now it's decision time.
"Does he want to be like Thierry Henry, who left Arsenal for Barcelona and won the Champions League? Or Jamie Vardy, who stayed at Leicester when he was coveted by other clubs and could have won more silverware but will be remembered as the Foxes' greatest player?
"One thing looks clear. From this summer onwards, future offers will be harder to come by. So I do think he should twist rather than stick."