Both players have enjoyed success elsewhere early in their blossoming careers, seeing their transfer values rise considerably over the last 18 months.
Jesus made the move from Brazilian club Palmeiras to Manchester City for £27m earlier this year, while Mbappe will finalise a £160m switch between Monaco and Paris Saint-Germain at the end of the season.
United legend Giggs believes that his former side missed a trick by overlooking the talented duo, who were available to purchase for as little as £5m at the time.
"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," he told The Times. "It was just like 'get them'. It would have been £5m or something - get them, loan them back - and that's where the recruitment could have been better.
"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 players and shouldn't have left. I'm talking about Rafael [Da Silva], Danny [Welbeck] and Jonny Evans - players who are United through and through.
"It was hard because Louis [van Gaal] had his own ideas and you had to respect that, but, yes, we had a few arguments about a couple of them. He understood because I had played with those lads, but they just weren't for him. Some of them, like Welbeck, wanted to play more regularly, and Jonny had a few injuries at the time, so you could understand it, but - and it's not saying it in hindsight - recruitment hasn't been great either."
Giggs left his coaching position at Old Trafford in 2016 to bring his 29-year association with the club to an end.