Television station Deportes Cuatro said the Premier League champions were willing to pay the 36 million euros Athletic insisted upon for the 24-year-old.
United would not comment on the reports when contacted by Press Association Sport, with Deportes Cuatro further claiming that the deal involved the Red Devils playing a friendly at Bilbao's new San Mames stadium in 2015.
Herrera played twice against United in 2012 as part of the Bilbao side that was so impressive in dumping them out of the Europa League.
Although his tally of two goals in 63 Primera Division appearances is not that impressive, United manager David Moyes feels Herrera can add the drive to his midfield which was notably absent during Sunday's 1-0 defeat at Liverpool.
At present exchange rates, the transfer would cost ?30.53million, just less than the club record ?30.75million United paid for Dimitar Berbatov in 2008.
The transfer would not be completed without some complications.
After all, the player would either need to have a medical in Spain, or fly to England for the checks to take place.
Whilst there is time for the deal to be completed, there is not much leeway for any late hitches.
Long-time target Marouane Fellaini also remains on Moyes' radar, although the Belgian's likely transfer seems to be wrapped up in a complicated web of deals that includes Everton's attempts to sign James McCarthy from Wigan and Fernando from Porto.