The 24-year-old has not won a major honour with Spurs and former player and coach, Sherwood, says that will need to change this season if they are to ward off interest from Europe's biggest clubs.
"There's only so much loyalty someone can show," he told The Debate on 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."