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 euros (£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: "Yes we received an offer last night [Thursday], an offical 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.
"We received the offer from Manchester last night and what we told them was we don't negotiate for our players."