The 30-year-old has one year left on his contract with Spurs, where Kane is the club’s record goalscorer.
Bayern reportedly had a bid of 100 million euros ($110 million) for Kane accepted on Thursday, with the decision on whether or not to leave left to the player.
Several British media reports now suggest Kane is heading to Germany for a medical.
Kane has never won a major trophy but appears set to join a Bayern side who have won 11 straight Bundesliga titles.
Thomas Tuchel’s men kick off their season against RB Leipzig in the German Super Cup on Saturday, before Spurs face Brentford in their Premier League opener on Sunday.