Former Chelsea scout Serge Daniel Boga says he spotted Mbappe while he was playing for French side AS Bondy as a 14-year-old and invited the youngster to trial with the Blues in 2012.
Mbappe performed well at Chelsea, playing in a 7-0 win over Charlton, but a move failed to materialise for the striker after the Premier League club attempted to arrange a second trial, which angered the player's mother.
"Chelsea were the first ones to give him a trial. We did it before Real Madrid," Boga told GOAL.
"I had a friend who worked for Nike, Denis Chantron, and when I was in France, we met and he said 'Have you heard of this young boy called Mbappe? He plays for Bondy, this small club from the suburbs of Paris.'
"I said I hadn't and he said 'You have to watch him.' I went there and watched him and I called him back straight away and I said 'Listen, this boy is really something.'
"I told Chelsea about him and let them do their thing. I called everyone at Chelsea whom I dealt with, like Jim Fraser. I said 'Listen, I have this kid you have to look at.'
"I brought him over with his family. He was skilful, like he is now. He played against Charlton and won 7-0. After a week at Chelsea, we went into the office. We said 'Listen, we appreciate what we saw from you but we have to invite you back for another trial and we'll see after that.'
"I remember what the mother said to this day. She spoke in French to Fraser and I was translating. She said to me, 'Listen, my boy won't be coming back. If they want him they have to take him now or in five year's time they will be coming back to buy him for €50 million!'
"That's what she said to me! I said, 'No I can't say that to them. It is too cocky for me.' She was right, though. It wasn't even €50m but €180m that someone would pay. So, she knew the quality of her son and she was right."
Mbappe would instead join Ligue 1 side Monaco, making his professional debut for the club in 2015 aged just 16.
He would help the principality win the French league title in the 2016-17 season before moving to PSG at the end of the season in a transfer worth €180m (£154m), a world-record fee for a teenager.
Mbappe has since gone to score 170 goals in 216 games for PSG, winning a further four Ligue 1 titles at the Parc des Princes.
He recently became the highest-paid player in world football after signing a new three-year deal in Paris worth a reported £1m per week – rejecting the chance to join Real Madrid on a free transfer.
In hindsight, Chelsea made a huge error in asking Mbappe to have a second trial at the club.
"He was very skilful but in England they want to see the player track back and be a hard worker. At the time, he wasn't a hard worker," Boga added.
"Defensively, he wasn't there yet. When he got the ball, he was unbelievable, but without the ball, he didn't work a lot. Chelsea wanted to see him again to see how he could improve on this. I think that's why they asked him back. He did skilful things and dribbled well.
"So, maybe the things they wanted to see in the second trial was improved work on the defensive side. They should have signed him. To be fair, though, it is easy to say that now. But, at the time, Chelsea had a good squad.
"Still, Mbappe is the best player I have ever scouted. I am proud, very proud to see what he has become. When I see him play, I say, 'Wow, my eyes were good!'
"He is the type of player that everyone wants to watch play. He has everything needed for a modern player. He is fast and in front of goal he is a killer. He has everything to remain one of the best players in the world for the next 10 years."
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