It has been widely reported that Mbappe wants to further his career away from the French capital and will look to leave next summer.
Liverpool, Manchester City and Real Madrid have all been linked with moves, though it’s expected any deal will not come cheaply.
He still has just under two years left on his contract so a fee would be required while Mbappe is expected to demand large wages.
Liverpool have been regularly linked and even more so following their deal with US sportswear giants Nike, though it appears the Reds are not interested.
Respected transfer journalist Fabrizio Romano told Oddschecker: "We’re talking about teams like Liverpool, Manchester City and Real Madrid looking at Mbappe.
"Right now, there has been no contact from Liverpool to get Mbappe next summer.
“We’ll have to wait some weeks to understand the real situation. Liverpool are not working to get Mbappe next summer."
It could all change in a year though and Mbappe has been told that he could be a real success at current Premier League champions Liverpool.
Former France international defender Willy Sagnol told Bild: "This club has a big advantage.
"With Klopp you have a coach with whom every player in the world would like to work.
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"Mbappe would have to adjust under him: he demands a lot of defensive work from his strikers, which Mbappe is not yet good at.
"But he can learn that, especially from a guy like Klopp. No question, Mbappe could become a king with Jurgen Klopp at Liverpool.”
Liverpool have strengthened this summer with Thiago Alcantara, Diogo Jota and Kostas Tsimikas all arriving at Anfield following their maiden Prem crown last season.