Real has not made any offer for him yet so if Liverpool goes and pays a bit more for him I think they can still get him and I believe that if Liverpool gets a player like Mbappe to join them they will be fighting for the title this year and they can have a go also in the Champions League because Mbappe for me is the best player playing in Europe now that the best ones have moved away to Saudi and USA.
Liverpool should act fast as Mbappe himself wants to go to Real so Liverpool should convince him with a really nice offer,personally I want to see him in Liverpool and the Premier League.
It's not about who has made the offer and who has not. Can Liverpool buy him if they make PSG a bid below or 100m? I don't think so... PSG value him at least more than 150m Euro and they want to get back that value out of his sale. Until they get that amount I don't think so that they are going to sell Mbappe. Can Liverpool match that? - is a big question but given so far how much they have spent, I don't think Mbappe is in their plans (I could be wrong though).
Also even if they match that value they also have to convince the player so that's another thing they have to work on. I am inclined towards Mbappe to Madrid right now but not in this transfer window and maybe next year.