Thomas Müller claims he rejected an “astronomical” offer to join Manchester United this summer.

Louis van Gaal has so far added Luke Shaw and Ander Herrera, with Marcos Rojo also set to join from Sporting Lisbon once he passes a medical and agrees personal terms.

Yet Müller, who starred in Germany’s triumphant 2014 World Cup campaign, stated he decided against a transfer to United. Asked by Bild if the 20-times champions had been close to signing him, Müller said: “Of course. I was aware that I could earn more by making that transfer. The amount that foreign clubs were offering me was astronomical. But Bayern are my club, a change was not an issue for me.”

However, United have denied making any such offer. A United spokesperson told the Guardian: “It is not true that we made offers for either Muller or Reus at any stage.”

The Atlético Madrid president, Enrique Cerezo, also claimed that Borussia Dortmund’s Marco Reus turned down the chance to be part of Van Gaal’s squad, with the Spanish club having been the subject of speculation as a potential destination for the German.

Cerezo said: “I don’t know where the Marco Reus rumour came from. It’s a player who, at this time, is impossible to us. Look, he had an offer for a lot of money from Manchester United and he has not gone. We will not sign him with a lesser offer.”

The claims suggest that United’s lack of Champions League football may be proving a hindrance in attracting elite level players required to rebuild Van Gaal’s squad.