Kane has been linked with a move away from North London following his recent comments about his personal ambition, and Manchester United are said to be among his suitors.
Rose, who is currently on loan to Newcastle United, has shrugged off talks of a possible £200 million transfer deal for his compatriot.
The Leeds United academy graduate hopes Kane’s performances will be rewarded with trophies at club level and has revealed that losing is anathema to the 26-year-old even when it is in the training ground.
"With Harry, we all hope his goals and his performances will merit a trophy one way or another during his career, but Tottenham means the world to him," Rose told the Lockdown Tactics podcast.
"We know that and when you see him disappointed, it's just one of those things that when you're on Harry's team in training you win. It's not a coincidence.”
"You just don't want to be on a losing side when you're on Harry's side, even in training. He's got that aura that you want to do the best you can."
Kane has established himself as one of the deadliest marksmen in Europe due to his goalscoring exploits in Tottenham.
He has netted 136 goals in just 198 Premier league appearances for the Lilywhites, making him the third highest scorer for Spurs in the English topflight.