The Spurs star reached an agreement on personal terms with the Bundesliga champions on Thursday evening.
Bayern agreed a fee of around £86.4million with the north London side earlier in the day as they close in on a move.
However, talkSPORT understands Spurs chairman Daniel Levy has tried to change the terms of the deal at the 11th hour.
Despite conflicting reports, Kane is set to be allowed to travel to Germany ahead of a move.
The 30-year-old now looks destined for silverware with Bayern, but Carragher believes he should stay in the Premier League.
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"Alan Shearer's PL goal record gets talked about a lot more than his PL winners medal," he said on Twitter.
"That record will be huge for HK. The big plus for going to Bayern is to guarantee he plays CL football & a chance to win that trophy every season.
"It's not about their domestic trophies, they'll win them anyway & I'm sure he'd rather have the PL record than the Bundesliga!"
But Ferdinand, who has clashed with Carragher on numerous topics this year, appeared to hit back.
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He also took to Twitter and said: "You don't start ya career saying you want to win the golden boot winner - you want to win things for ya team.
"You only make it personal honours when that's ya only option!! Good luck Harry Kane."
Many would have thought that Kane would have opted to stay at Spurs in order to exceed Alan Shearer's Premier League goal record.
He is currently just 48 goals from taking the crown for himself, but Shearer looks set to hold onto his achievement for even longer.
Instead, Kane will join a Bayern side who will be searching for their 12th consecutive Bundesliga title.
He will also have a shot at winning the Champions League once again having come so close with Spurs in 2019.