Kane is the subject of huge interest to Bayern Munich this summer while Chelsea and Manchester United have been linked with moves for the England captain.
The 29-year-old has just a year left on his contract in North London but at the twilight of his career has no trophies to show for his efforts.
Having come through the Spurs youth system, Toure, who recently left his role as an academy coach at Tottenham, feels Kane remains indebted to the club and should stay put.
“Harry Kane is a brilliant player and a brilliant leader,” the 40-year-old, who has just taken a coaching job at Standard Liege, told the PA news agency.
“For me I hope he is going to stay at Tottenham. What he did last season was incredible.
“I hope he is going to stay, being involved with the staff I can see how familiar they are, they all believe in each other.
“He came from the academy, he is different. He is not like (Sergio) Aguero, who came in from Atletico, he is at home.
“I hope he is going to stay because he is a good player. Why not retire there, like (Paolo) Maldini or Gerrard did at Liverpool, if he does that it is going to be very significant.”
Tottenham have not won a trophy for 15 years but Toure is adamant success is not too far away from the club.
“Tottenham have everything to be successful, when you see the stadium and facilities, they are brilliant,” he added.
“What’s left now? Maybe change players, I don’t know.
“But the competitiveness of the league, you have to match that. “What Manchester City are doing, you have to match that if you want to win.
“That is what I learned when I was at top clubs, week in week out, try to improve the club to be successful.
“I hope and believe that if Harry Kane stays, new players will join, the club will be improving and better and they will be able to challenge for something.”
