Kane has been in blistering form for Spurs this season, with 29 goals in all competitions, and made a dream start to his England career on Friday by scoring just 79 seconds after being introduced as a substitute in the 4-0 Euro 2016 qualifying win over Lithuania.
England manager Roy Hodgson has confirmed that Kane will be afforded his full debut in Tuesday's friendly against Italy in Turin, and Vassell - who netted six goals in 22 England appearances and also scored on his international debut in a 1-1 draw with Netherlands in February 2002 - is predicting big things for the 21-year-old.
"The sky's the limit," he told Perform.
"Once you get your foot in the door and you're confident and proved you can do it at the highest level, it's down to you as a person.
"Ability-wise, I don't see why he can't become England's main striker in the future."
Kane's goalscoring exploits have thrust him into the spotlight and expectations are high, but Vassell hopes the people around the young forward will help him cope with the pressure.
He added: "It's difficult. It boils down to the people you've got around you. Obviously scoring on your debut is a dream come true so he'll be thankful for that.
"The people around him have got to keep him grounded and keep him doing the things he was doing prior to that.
"Touch wood he stays injury-free and I don't see why he can't take it all the way and play for England at a major competition."
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