The Premier League champions have launched a big-money bid for the former Spain Under-21 international after being frustrated by Everton's stance over Marouane Fellaini
Manchester United have had a £25.5m bid for Ander Herrera rejected by Athletic Bilbao.
Athletic chiarman Josu Urrutia confirmed on Friday that he has rebuffed a bid from David Moyes' side, who have 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.
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The move comes as Everton continue to play hardball over Marouane Fellaini - and Leighton Baines - following a summer in which United have missed out on primary targets Cesc Fabregas and Thiago Alcantara.
While the club's Fellaini hopes are not dead, they have started to broaden their search with Monday's transfer deadline looming.
Ander's release clause stands at €36m (£30.75m), and Athletic have told the Premier League champions that they must match that figure if they want 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 €40m (£37m).
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.
A club source told Goal: "David has always been a massive fan of Ander's, having monitored him since his time at Zaragoza."
The Scot was unwilling to give too much away in his weekly press conference at Carrington: "I wouldn't disclose any names, just let the clubs deal with it and we'll try to do it on a professional manner.
"I don't know how busy it's going to be but it's a busy football market. It might be busy in the next few days and I hope we do a little bit of business but I couldn't guarantee that."
Ander 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.