Like avoiding such rumours Because despite Mbappe being offered so much money, he is only thinking of leaving PSG with the hope of winning the Champions League trophy and the Ballon d'Or, why would he sign for that money with a team like Liverpool who have not already qualified for the Champions League? The biggest and most likely of all the rumors is Mbappé's move to Real Madrid. If Mbappe does decide to switch clubs, he is most likely to join Real Madrid. And this possibility may be true. Also I don't think Mbappe can join Liverpool.
Winning big titles like Champions League and domestic titles at leagues which are bigger than Ligue 1 are Mbappe's targets. Especially Champions League which is a most wanted title with Mbappe and he knows that winning Champions League is a big achievement for his career even he already won World Cup 2018 with France. Additionally, winning Champions League will open a very big chance for Mbappe to win Ballon d'Or which he has never won in his career.
Though titles are important for Mbappe's consideration, we can not exclude that he also want to receive good salary. He deserves that and he will not join a club that pay him like $1M or $4M each season even he can win Champions League with them. Titles with a team, personal awards and high salary are all factors for Mbappe consideration about his next destination.
If talking about chance to win Champions League, Liverpool have less chance than Real Madrid.