Manchester United made a world-record bid for Bayern Munich's Thomas Muller last summer, according to chief executive Karl-Heinz Rummenigge.
Manchester United were repeatedly linked with a move for Muller in the British press, and Rummenigge admits an offer was put in by the club, who were managed by Louis van Gaal at the time.
But speaking to German publication Frankfurter Allgemeine Zeitung,Rummenigge said the offer was not considered for one second.
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"We had a mad offer from Manchester United last year, which was not a topic for one second. We could have secured a world-record transfer fee.
"Thomas Muller came out of (the youth academy). (He is) born near Munich, formed here, the hero of the fans."
Rummenigge also revealed that Bayern had the chance to sign Kevin De Bruyne from Wolfsburg last summer, before the Belgian midfielder eventually moved to Manchester City for £54.5m.
"We had an offer to sign De Bruyne in 2015 for the following year," Rummenigge added.
"The fee plus salary amounted to over 100 million euros, so the risk was too high. We have now signed a center-back in Mats Hummels, because we have enough quality and quantity in attack."