The former United winger and assistant coach said he recommended both players to be signed during Louis van Gaal reign, but both slipped through the net.
Ryan Giggs: Manchester United missed out on Mbappe and Jesus
Ryan Giggs says he advised Manchester United to sign Gabriel Jesus and Kylian Mbappe before the pair rose to prominence.
Former United winger Giggs joined the club's backroom staff when his stellar playing career drew to a close, serving as Louis van Gaal's assistant after spending a year as player-coach under David Moyes.
And Giggs, who watched Brazilian striker Jesus and France forward Mbappe with a scout during that time, believes the club's recruitment "could have been better".
He told The Times: "I watched Gabriel Jesus play three years ago. I watched Mbappe for a year.
"I was watching them with the scout and it was a no-brainer. It was just like, 'Get them'.
"It would have been £5 million (Dh24.5m) or something - get them, loan them back - and that's where the recruitment could have been better."
Jesus joined Manchester City for a reported £27m in January while Mbappe swapped Monaco for Paris Saint-Germain this summer, initially on loan but with an option to make the move permanent next summer for a fee of around £166m.
Giggs also thinks some of the players United let go should never have been allowed to leave the club.
He added: "I know what a Manchester United player looks like.
"There have been a lot who have come through that haven't been United players and also players who were United and shouldn't have left.
"I'm talking about Rafael (Da Silva), (Danny) Welbeck, Jonny Evans - players who are United through and through.
"It was hard because Louis had his own ideas and you had to respect that but, yes, we had a few arguments about a couple of them."