The 24-year-old has scored at least 20 goals for three consecutive Premier League seasons and already has six for club and country in all competitions so far in this campaign.
However, despite his impressive goalscoring statistics, the England striker has not won a major honour with Spurs and Sherwood believes that will need to change this season if they expect to stop Kane from moving to one of Europe's biggest clubs.
"There's only so much loyalty someone can show," he told 'Sky Sports'.
"Tottenham have been a great club for Harry and he's been paying them back tenfold. He's been outstanding over the last couple of seasons, he grew up a stone's throw from the ground and the kid loves the club.
"But that only lasts a certain amount of time. Then he starts seeing the pound signs and sees the likes of Barcelona, Real Madrid or - dare I say it - Manchester United - and then your head gets turned.
"The only way they can keep him is to win something this year. That something might not be the Carabao Cup, it might have to be the league or the FA Cup."
Kane signed a new deal with Tottenham last December which is reported to be worth around £90,000 a week with up to £30,000 in bonuses and lasts until the summer of 2022.
However, those wages are less than half of what some of the Premier League's top players earn and as the winner of the last two Premier League Golden Boots, Kane's head could be turned by offers from other clubs.