Reports have suggested United are set to pay around £30million for the 24-year-old Spaniard, who they tried to recruit last summer, before his fee rises at the end of this month due to the terms of his contract.
And it is understood the deal could be wrapped up in the next few days.
Herrera would become the first new signing United have made since they confirmed Dutchman Louis van Gaal - currently in charge of the Holland national team at the World Cup - as the permanent successor to sacked manager David Moyes in May.
Moyes' attempts to secure Herrera's services for the Red Devils last summer descended into farce on transfer deadline day.
Reports emerged of three people, said to be representing United, managing to get into Spanish league headquarters for discussions about the proposed switch and then leaving an hour later, apparently unable to complete the paperwork required to finalise the deal.
It subsequently transpired that United, who dealt directly with Athletic, knew nothing of the trio's existence. Negotiations between the two clubs collapsed anyway, with Moyes believing the buy-out clause in Herrera's contract was too high.
Just under a year later, though, it seems talks have been revived and are set for a swift conclusion.
Herrera, who played for Real Zaragoza prior to joining Bilbao in 2011, has been capped for Spain at under-21 level and also represented his country at the London 2012 Olympics.