The Red Devils tracked the 24-year-old playmaker for much of last summer, but ultimately failed to lure him away from the Basque side during what was a thoroughly disappointing transfer window for them.
Herrera has a buy-out close of around £30m, but United will have to act quick as by the end of that month the figure will rise to around £35m.
Despite having snapped up Juan Mata in January under the guidance of David Moyes, the 2012/13 Premier League champions are keen to add further creativity to their ranks, and see the silky passer as a top signing.
The player himself was thought to have been against a move to Old Trafford last year, but his stance may have swayed between times even though the San Mames side managed to finish in the top four in La Liga.
Herrera has been an ever-present in the Bilbao first-team since his 2011 arrival from Real Zaragoza, but his impressive performances have not, as of yet, been enough to force him into the Spanish senior international side.