Sport says United had been chasing Traore's signature since the days of David Moyes - and Louis van Gaal's appointment had not changed their thinking.
Talks were held with Traore's camp about a move to Carrington before Monday's deadline.
And in mid-August, the winger's agents met with Barca coach Luis Enrique and sports director Andoni Zubizarreta to discuss his future.
The pair made it clear how much they valued Traore and his place in Enrique's plans. That was enough for Traore to reject United's offer, but they'll be back if the youngster finds his path to the first team blocked.
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