The 20-year-old was United's top target but they weren't prepared to meet Borussia Dortmund's £108million asking price.
The Ivorian winger who holds the record for the youngest goalscorer in Serie A last season will join the Red Devils in January.
If United are successful in agreeing a deal for Traore, it is expected that the player will stay with Atalanta until January.
When deadline day arrived, Man Utd turned their attention to buying for the future and they entered advanced negotiations with Atalanta over a deal to sign exciting teenager Traore after registering their interest earlier in the summer.
United were first alerted to his talent in 2016 when a scout reported on his performance in an Under-15s game.
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With United's pursuit of Jadon Sancho and efforts to secure a loan deal for Barcelona winger Ousmane Dembele not coming to fruition, it is likely that these teenage wingers will be the only additions in that position, with time running out to bring in anyone else.
"There are defenders in the first-team that sometimes can not stop him".
The Premier League club will play €30 million (£27 million) plus add-ons for the Ivory Coast prospect.
'The club need to have valid reasons to take him to the UK. One reason is that the player is coming from a top team and with Atalanta [having] been playing global competitions over the last few years, there are no problems to prove it.
"[Diallo] still needs to get a work permit since he has not played with his national team yet".