No player scored more goals than Kane in the Premier League in 2015 - but Wayne Rooney did not even get close, netting an embarrassingly low number.
Carragher said, speaking on Sky's broadcast after Liverpool's win against Sunderland on Wednesday night: "If he carries on that form to the summer, he will put big pressure on Wayne Rooney to be the star."
Yet there is a case to make that Kane should already be regarded as the star, and Rooney as the one who has it all to prove.
His form has been woeful this season, with his England goals record distracting from that - mainly achieved with goals in qualifying matches and friendlies against low ranked nations.
Kane of course must maintain his form going into Euro 2016, but Rooney needs to find his, and if the challenge of Kane cannot inspire him to do so then it is very much time for manager Roy Hodgson to be worried.
With Jamie Vardy netting 19 league goals in 2015, and Danny Welbeck and Daniel Sturridge both hoping to return from injury in time to make the squad, Rooney cannot afford for his second half of the campaign to be as embarrassing as his club record in 2015.