United had a £25m offer knocked back by the Spanish club earlier this week, and Athletic reportedly told the Old Trafford side that only a €36m bid will be considered.
That's Herrera's release clause, and although Bilbao are desperate to keep the young midfielder, they're powerless to stop him holding talks with United once the Premier League champions trigger his buyout fee.
The 24-year-old was left on the bench during Bilbao's defeat to Real Madrid, although Bilbao manager Ernesto Valverde insisted after the game the decision had nothing to do with interest from United.
Sky Sports La Liga expert Guillem Balague tweeted: "United have offered 36 for Herrera. Herrera will have to pass medical and United pay it all in cash but deal practically done."
The Spain under-21 international was part of the hugely impressive Bilbao team that took Manchester United apart in the Europa League two seasons ago.
The La Liga club suffered a disappointing campaign last term, but Herrera remains one of the most highly rated young central midfielders in Europe.
United have been linked with a whole host of names this transfer window, with the central midfield position a particular need.
Daniele De Rossi and Marouane Fellaini have also been strongly linked within the past seven days, but it appears Moyes has targeted Herrera as his top transfer priority on deadline day.