Throughout the last month, it has been widely claimed that the Bundesliga champions are intent on securing a deal for the England international.
Spurs' all-time leading goalscorer now has less than 12 months remaining on his contract and has shown no indication that he is open to penning fresh terms.
Despite the persistent firm stance of chairman Daniel Levy, recent reports have indicated that owner Joe Lewis has informed Levy to agree fresh terms with Kane or cash in on his signature.
At one stage, Bayern were regarded as no more than outsiders, particularly when they had a bid of €80m - their second formal offer - rejected for the 30-year-old.
However, that no longer appears to be the case, it increasingly likely that Bayern will eventually reach a compromise with their Spurs counterparts over a fee.
Nevertheless, according to Sky Sports News, Bayern are still not close to finding a number that will see Spurs sell their most prized asset.
On Monday, the relevant parties are said to have held discussions over what would be viewed as an acceptable proposal, with talks allegedly continuing into the afternoon.
That said, the report says that Bayern are still at least £20m away from making the breakthrough, increasingly the pressure on club officials to up their offer.
Although Thomas Tuchel is well stocked for options in the final third for the opening weeks of the season, he is still eager to add Kane to his ranks as soon as possible.
There could theoretically be progress when Sadio Mane completes a transfer to Al-Nassr, Bayern standing to generate £34m from the sale of the Senegal international after just one season at the Allianz Arena.
Spurs are allegedly insistent on a buy-back clause in the event that Kane contemplates a return to the Premier League later in his career.
Levy has previously prevented Kane from signing for the likes of Manchester City and Manchester United with the Spurs chief against strengthening a top-flight rival.