The Premier League champions had expressed a strong interest in signing the 25-year-old during the January transfer window but failed to agree a deal with Shakhtar.
Guardiola is said to have been impressed with Freds performances against City in the Champions League this season.
But according to UOL, Guardiola has now ended his interest in Fred and has made the signing of Napoli midfielder Jorginho his priority.
The report also claims that sources close to negotiations believe United is now Freds most likely destination.
Earlier this week, it was reported that Shakhtar are looking to hold out for United to activate the Brazil internationals £53 million release clause.
Speculation surrounding Freds future also increased last week when his Shakhtar teammate Darijo Srna revealed that the midfielder is heading to Manchester this summer – although he did not elaborate whether that meant City or United.
Fred also confirmed this week that his future is unlikely to be resolved until after Brazils World Cup campaign.
More: Manchester United FC