The Spanish central midfielder's contract is up in the summer and it is believed that talks over a new deal have hit a standstill.
'Sportsmail' understand that the offer on the table has fallen short of Herrera's expectations and he is now considering his options.
This leaves him potentially free to talk to clubs outside of England in January, one of which could be his former employers.
Herrera left the San Mames in 2014 for a fee of £29million, but now could return to the Basque club for free if he lets his contract run down.
It is believed Bilbao would make him their highest played player, with their rule of only recruiting players born in the proud region making the transfer of the upmost priority.