The Reds are among a host of Europe's top clubs to have been linked with the 18-year-old, who has enjoyed a fantastic breakthrough campaign for Monaco, helping them win Ligue 1 ahead of Paris Saint-Germain this year.
Mbappe's 15th league goal of the season against Saint-Etienne helped his side secure the title this week and a report in Marca on Thursday claimed Liverpool had been in contact with Monaco to make an official £65m bid that they say was turned down immediately.
The Reds are interested in the teen sensation, who also scored 11 goals in other competitions for Monaco this term, including six in their run to the Champions League semi-finals, but it's believed no bid has actually been lodged yet.
Manchester United, Real Madrid and Barcelona are all also watching the situation closely and could make moves for Mbappe this summer, who is already valued in the £60-70m bracket following his stunning performances.
The youngster is under contract at Monaco until summer 2019 and has previously said he would like to stay at the club for another year, while billionaire Russian owner Dimitri Rybolovdev has made it clear he is in no rush to sell the in-demand striker.