Herrera was reported to have flown to Manchester to finalise his move to Old Trafford but Athletic have now taken a firm stance by issuing a statement confirming they have rejected the offer from United.
The gifted midfielder, also a target last summer for former manager David Moyes, has a release clause of €36m but in order to activate it the player would have to effectively buy himself out of his contract.
Bilbao's statement says they have rejected United's more conventional offer - which matches the value of the clause.
It is understood that Herrera's release clause rises to €40m on July 1.
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