Bayern Munich are desperate to sign the 29-year-old after making a striker a priority, with the German giants flying over executives to try and thrash out a deal.
The England international has one year left on his contract and his future looks more unclear than ever.
He has yet to commit his future to Tottenham - fuelling rumours that he could be on his way out of north London this summer.
Kane's former Spurs teammate Rose was in the talkSPORT studio on Thursday where he gave some insight into his old pal.
And the left-back admitted that a move to Bayern would not be his priority - though he can understand why Kane would want the transfer.
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Commenting on Kane's potential switch to Germany on talkSPORT Drive, Rose remarked: "If you was going to ask me the teams I would think of that Harry would join, I wouldn't have said Bayern is one of the first ones I'd choose from.
"But saying that, you fully expect Bayern to be in the quarters or semis of a Champions League each year. You expect them to win the league, so I don't see why not.
"You [talkSPORT host Darren Bent] know coming from Spurs, that Spurs doing business with the top teams in England is very rare."
He added: "Tottenham to Chelsea is just never going to happen, so after that, you have to look abroad and if I'm Harry, yeah I don't think Bayern is a bad one."
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Rose continued: "If you said Bayern, I wouldn't have put them as my top three teams.
"But as I said, Harry going anywhere in England, it's going to be really, really difficult.
"Definitely I can't see the Chelsea one because the two clubs don't do business historically, and I don't know if Harry's legacy at Spurs would get a bit tarnished.
"I know the fans definitely know if he was to leave you could never, ever blame him, but try not to go to Chelsea with all respect.
"Tottenham to [Manchester] United, it's only been [Dimitar] Berbatov from my time at Spurs."
Indeed, Spurs chief Daniel Levy has been reluctant to sell Kane to Premier League rivals - as exhibited in 2021 when he stood firm over Manchester City's pursuit of his talisman.
United have long been interested but have not entered the race for Kane, who turns 30 on Friday, partly due to Levy's stance.
However, if a deal is not agreed with Bayern, there is a strong chance that Kane leaves Tottenham next year on a free transfer.
Then the Englishman can pick whatever club he wants, something Rose also alluded to.
He said: "Tottenham can say, 'we're not going to let him go for free,' but if Harry says, 'hold on a minute, I'm not going anywhere'.
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"They're not going to treat him how they did me, they're not going to put him with the reserves.
"They're not going to do that to him, they're not going to take his number away from him, so Harry holds all the cards."