The club from Bizkaia are reported to be putting together an 'attractive proposal' for Herrera, who came through the youth ranks at San Mames.
Herrera made 94 appearances in the league for the senior side before moving to Manchester United for €35million in 2014, and Bilbao are planning to lure him back as part of a big summer shakeup.
And despite the fact that Herrera has made 23 Premier League appearances, as well as scoring the winner against Tottenham in the FA Cup semi-final, he is one of a number of players who could leave Old Trafford.
The Basque side have had a disappointing season, currently sitting 14th in the table.