Liverpool is trying to get mbappe as loan from PSG but i don't even think PSG wanna give mbappe's remaining contract as loan to the liverpool. PSG will prefer to sell him as permanent status instead of giving him to the liverpool as a loan. It's a trick by liverpool.
Mbappe will not move to Liverpool. This story will end up like just every other story about where Mbappe will end up. Real Madrid is the destination that Mbappe wants to get to, but along the way to the club, the choice of club to play for is difficult. Mbappe does not fit the Liverpool style of play even if it is for just one season, Liverpool are just trying their chance to see if it will work, but it won't.
We shouldn't believe the rumors on this one the media just want to attract the attention of visitors without a clear source. As you said Mbappe will only move to Madrid no chance for any other club including Liverpool , if we look at Liverpool's transfer history their average budget each season is between 150 to 200 million and this season Liverpool have used 112 million then I'm sure they won't spend more and maybe Liverpool have closed their transfer book this season. Instead I even heard rumors that Moh Salah will move to Milan , is it true? I hope this is an empty rumour.