Athletic said they dismissed a bid from United on Thursday night that fell short of the buy-out clause in his contract, and stressed there was no room for negotiation.
Club president Josu Urrutia said in a press conference on Friday that any player can leave the club, but only if he indicates a desire to go and his full release clause is paid.
In Herrera's case, that clause is widely reported to be 36million euro (£30.75million).
Urrutia indicated Athletic would wish to keep Herrera, a Basque player born in Bilbao who began his career at Real Zaragoza.
Urrutia said on Friday: "Yes we received an offer last night, an official offer from Manchester United. When there's something I'll confirm it.
"Our club is different, our club is special, it's based on sentiment.
"Our objective as a club is not to make money through our players, but to have the best performances possible.
"To break a contract with Athletic, first they have to tell us they want to leave, and that's not the case with Ander, at the moment. Then they have to pay the buy-out clause in his contract, and that's not the case here either.
"In reality the buy-out clause in Ander's contract has not been met.