Chesterfield's chief executive Chris Turner said that he is expecting bids for Darikwa in January and that they will have to go way beyond the club-record fee of £750,000 received for Kevin Davies from Southampton in 1997.
"Tendayi is attracting a lot of attention and there is no doubt in our minds that he will go on to play at a higher level," Turner said. "For a manager of Manchester United to come and watch a League Two game just shows that David has his finger on the pulse.
"I know when he was Everton they regularly watched Tendayi so you would assume he knows all about the best young players in the lower leagues.
"I knew David was coming to the game because I had spoken to him before, although we didn't mention individuals. Having said that, Tendayi did have an exceptional game on Saturday so he can't have failed to notice him anyway."
Darikwa, who signed a new three-year contract at the Proact Stadium last year, joined the club as a 16-year-old after unsuccessful spells with Nottingham Forest and Notts County.