The way I see it, Bayern Munich is going to sign Kane because they will be meeting with Tottenham again to discuss transfer fees, and I think Bayern Munich will be well-prepared to ensure that the deal is completed because if Bayern Munich and Tottenham couldn't come to an agreement this time, Manchester United would take advantage of the situation to sign Kane since Manchester United also needs a striker player. Although Manchester United still has good players, I believe the team also needs a goal-scoring player like Kane. I also heard that Manchester United sent a later indicating that they want mbappe too, which surprises me. How will Manchester United be able to afford the cost of purchasing mbappe?
So, now the agreement between Bayern Munich and Tottenham is getting closer regarding Kane, because in my opinion there really is no other choice that Tottenham can choose if they don't want to suffer losses by leaving as a free agent. Then on the other hand Kane has not taken a decision to extend his contract. This means that it is indeed very appropriate to take a put option in conditions like this. If we take a look at some of the recent news regarding Kane's move, it looks like this will be happening soon, and we're just waiting for a formal deal to be announced. Meanwhile, on the other hand, Manchester United also need a new striker, as you said, and they have been hunting Kane for a long time. However, after I read the latest news, Manchester United are now having doubts and are a little pessimistic about their goal of getting Kane because of negotiations that have not been completed. But if Tottenham are now willing to let go of their flagship player, it looks like this will make it a little difficult for Bayern Munich to be able to bring in Kane, because it is clear that if the transfer fee proposed by Manchester United is higher then it is likely that Tottenham will let him go for Manchester United.
Even though I am unsure of the team's finances and am unaware of the specifics of its bank accounts, I do not believe that Manchester United will be able to purchase mbappe. Even Barcelona Real Madrid, where mbappe wants to transfer, has not reached an agreement with PSG because Al-Hilal has made an offer of $300 million to purchase mbappe, and I believe that this sum is not insignificant.
For Mbappe himself, I don't think Manchester United will be able to pay such a high transfer fee, because we know now that Manchester United themselves are not very good in terms of finances and for Kane it seems that it is still possible for them to catch up. I think at the moment it is better to compete with Bayern Munich to get a deal for Kane because I think the arrival of Kane is also enough to be able to improve and sharpen Manchester United's performance.