I don't know Arsenal can or would like to spend hundreds of million euros to make a signing like this in the first place. Even if they do Mbappe wouldn't still choose Arsenal as long as Real Madrid make the same offer.
It all depends on the offer and Mbappe's decision to choose that, but we as a football fans know Real Madrid is more stronger and high likely will help Mbappe to reach his maximum capability. Mbappe could win Champions League and get Ballon d'Or easier.
It's also an honor for Mbappe to replace number 7 player in Real Madrid which one of them is Cristiano Ronaldo, there are many reasons Mbappe will move to Real Madrid rather than Arsenal.