The Premier League champion has launched a big-money bid for the former Spain Under-21 international after being frustrated by Everton's stance over Marouane Fellaini.
Athletic chiarman Josu Urrutia confirmed on Friday that he has rebuffed a bid from David Moyes' side, which has so far floundered in their attempts to attract midfield reinforcements to Old Trafford.
"There's an offer from Manchester [United] for Ander Herrera," Urrutia told reporters. "Our club is different, it bases itself on sentiment. Our goal is not to make money. We consider Athletic a unique club and the players have to think like that.
"We received the proposal last night, and we said that we don't negotiate for our players. For a player to leave, he first has to show that he wants to leave the club then deposit the clause."
The move comes as Everton continue to play hardball over Marouane Fellaini - and Leighton Baines - following a summer in which United has missed out on primary targets Cesc Fabregas and Thiago Alcantara. While the club's Fellaini hopes are not dead, it has started to broaden its search with Monday's transfer deadline looming.
Ander's release clause stands at 36 million euros, and Athletic has told the Premier League champion that it must match that figure if it wants to sign the 24-year-old. The Basque club last summer insisted that Bayern Munich pay the full clause for Javi Martinez, who eventually moved to Bavaria for 40 million euros.
It is unknown whether United will return with a larger offer for the midfielder, who joined Athletic from Zaragoza in 2011, though manager Moyes is a long-time admirer, according to a club source..
Herrera has represented Spain at Under-20 and U21 level, as well as at the 2012 Olympics, but is yet to receive a call-up to the senior squad.