We have no officially news about this all even right now few things are clear again on transfer window too much drama and surprises are going to happen because this is beauty of the transfer window in every season currently we have few top ranked players which are going to have huge amounts and big influence on their transfers with Harry Kane, Kylian Mbappé and Victor Osimhen are top players.
Currently, nothing is clear because mostly clubs are working on few things after few days we will have clear updates Bayern Munich is strictly working on Harry Kane and Real Madrid is also working on their striker problem even mostly feeling they have no sources for the Kylian Mbappé so most chances he will enter in England for the next era and Victor Osimhen is also had good feedback from giants in UEFA so wait and watch for the next rumour who is going to leave his club for the another record transfer fees in this transfer window.
Honestly, I'm not sure Liverpool and Arsenal will bring in Kylian Mbappé the main reason is that the Premier League is not the next purpose he prefers LaLiga
Another reason I doubt they are ready to pay a high price and high salary, while Arsenal already have Kai Havertz with a salary 330k per week obviously it will interfere with their budget, the same thing with Liverpool they have several players with high salaries while for Madrid it makes sense they really need a striker even Mbappe has been targeted since last season.
Indeed, this sounds quite strange if Liverpool and Arsenal are interested in signing Mbappe, but that's okay, at least this adds to the excitement about the next Mbappe's future. I think there was no other reason for Mbappe than to join Real Madrid because he really wanted to win the Champions League and the Ballon D'or, that's what motivated Mbappe if he was more interested in Spain than England. After all, Real Madrid has everything to be able to bring Mbappe as the best player in the world and he will even get the highest salary every week.