The teenager allegedly visited Stamford Bridge four years ago but the club weren't interested, turning their focus to local academy prospects Dominic Solanke and Tammy Abraham instead.
Mbappe had been playing for amateur French side Bondy at the time, with Real Madrid also monitoring the youngster’s development.
According to the Daily Mirror, the forward’s representatives attempted to push the Blues into a move by telling the club that Real were poised to swoop but this proved unsuccessful.
Mbappe went on to hone his trade at France’s illustrious Clairefontaine academy before signing for Monaco in 2013.
Four years on, the 18-year-old has established himself as one of the most highly-sought talents in Europe – with Manchester United, Arsenal and Real, among others, all keeping tabs on the teenager.
Mbappe has enjoyed a stellar season in Ligue 1, with 22 goals to his name from 35 appearances.
As he prepares to help guide Monaco past Juventus in the Champions League semi-final, veteran goalkeeper Gianluigi Buffon praised Mbappe and suggested he could surpass Thierry Henry in terms of quality.
“Mbappe is an incredible talent and I think he seems like a good boy,” Buffon said.
“Of course the characteristics are similar [between him and Thierry Henry]. He plays for Monaco early in his career, the very slender and elegant running style.
“Probably, at his age, he is even better in front of goal than Henry was.”