The 24-year-old has already scored 11 goals in all competitions for the north London club, which include six goals in the Premier League and five in two matches in the Champions League.
The Tottenham striker's form has seen him attract interest from Real Madrid, while Manchester United have long been reportedly interested in signing him. Spanish journalist Eduardo Inda told El Chiringuito that the 12-time European champions will be interested in Kane and are well aware they need at least €200m (£177.4m, $236m) to make the deal a reality.
Shearer refused to give any career advice to Spurs star, but suggested that it would be important for Tottenham to win silverware if they are to keep him at the club.
"He will have options. The big boys will come calling. I am pretty sure of that. I would never tell him what to do. Only he will decide. It would help Tottenham dramatically if they go on to win anything in the next 18 months to two years," Shearer told IBTimes UK.
Kane was on the scoresheet for England during the international break as he scored against Slovenia and Lithuania in the last two World Cup qualifiers. The Three Lions have already secured a place in next summer's tournament in Russia.
Shearer says Kane has to play a vital role if England are to be "relatively successful" in the 2018 World Cup.
"Harry is the best. If England are to be relatively successful in Russia, he has to play really well. I would think that he will be named as a permanent England captain in the not too distant future, which will only enhance his confidence," the Premier League legend stressed.
"Well, there is no real expectation for England to win the World Cup in Russia. We have to improve from what we did almost two years ago in the European championship."