Real Madrid manager Zinedine Zidane is thought to be extremely keen on bringing Mbappe to the Bernabeu.
Zidane stated recently that the decision would be up to the player himself, which Paris Saint-Germain sporting director Leonardo was less than impressed with.
"It's annoying," he said of Zidane's comments.
"This isn't the time to speak about dreams and all of that. It has to stop. Mbappe is very important for us and this isn't the moment to destabilise him."
Jurgen Klopp is thought to be just as big a fan of Mbappe as Zidane is, and could push the Liverpool hierarchy to go all out in their attempts to sign him.
Madrid president Florentino Perez is reportedly becoming worried that the Champions League winners are capable of outbidding Los Blancos.
Mbappe joined PSG from Monaco on a permanent basis in 2018 for a fee of £120m (plus £40m for his loan the year before).
Now, Liverpool are reported to be readying a fee in the region of £250m to secure the 20-year-old's services.
It's believed that because the Reds didn't spend money last summer, despite winning the Champions League, they have cash reserves big enough to pull the deal off.
The report also claims that Liverpool are preparing a pay packet that would see Mbappe earn £34m a year, which is more than Lionel Messi earns at Barcelona.
Mbappe now has 79 goals in 104 appearances in Ligue 1 for PSG, but stated in May that he may be ready for a "new project".
The potential signing of Mbappe would probably mean the end for one of Liverpool's current front three.
Mohamed Salah is understood to be the likeliest to leave because of his 'bad' relationship with Klopp.
But the report goes on to suggest that Mohamed Salah may find a new home in Madrid.
It's claimed that Real will turn to Salah should Liverpool manage to land their first-choice transfer target Mbappe.
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