On this current price of Kylian Mbappé 180 Million pounds most chances these both big clubs not try because they are not interested on this high price as Real Madrid is now looking for few other options and Manchester United is also having suitable replacements on suitable prices even they are not good as Kylian Mbappé quality but still can do good for their club which is acceptable for them.
Now with the option of he is not going to extend his contract and PSG is never like to allow him as free agent how things will be gone in next few weeks it's interested because we have one more club which can jump into this, but It's not sure with Newcastle United which is newly promoted to Champions League and want to make mark, but surely they will also not go with this amount at the end we have only Real Madrid but as all know not on this price.
If someone offers 180 million euro for Mbappe, I feel like he will most probably be sold. In that case we would have to see Mbappe reject the offer, because one team offered it, psg accepted it, and it's all up to him at that point, if he rejects that team at that stage, then I am sorry but he won't join that team for free neither, but if he leaves for free next summer he will need to go somewhere.
So, I suggest Real make another 180 million offer, PSG most likely will accept that, or at worst negotiate on the price, and if they can get PSG accept it, we all know Mbappe would accept it, because if he rejects then he won't get a chance next summer neither, Real fans will think he didn't want them and management will not want to piss off fans.