Urrutia told a news conference Herrera, who has a contract until the end of the 2015-16 season, could only move if he informed the Spanish club he wanted to leave and United paid his buyout clause of 36 million euros (30.7 million pounds).
Sports daily Marca reported on Friday that United had offered 30 million euros for the 24-year-old, while As newspaper said the offer was worth 27 million.
"We received the offer last night and we have already said that we do not negotiate for our players," Urrutia was quoted as saying on Bilbao's official Twitter feed.
"For us Athletic is a unique club," he added. "The players are required to feel the same way."
If United's bid succeeded, Herrera would become the latest in a long line of Spanish player to move to England in the close season, following the likes of Jesus Navas and Alvaro Negredo to Manchester City and Roberto Soldado to Tottenham Hotspur. ($1 = 0.7562 euros)
(Reporting by Iain Rogers, editing by Ken Ferris)
